diff --git a/AscanValuesL.txt b/AscanValuesL.txt
new file mode 100644
index 0000000..d6a8b8a
--- /dev/null
+++ b/AscanValuesL.txt
@@ -0,0 +1,1250 @@
+-2032	-2032	-2016	-2032	-2032	-2016	-2016	-1984	-2016	-2032	-2032	-2032	-2032	-2016	-2032	-2016	-2000	-2032	-2032	-2000	-2016	-2032	-2016	-2032	-2000	-2016	-2032	-2000	-2016	-2032	-2016
+-1952	-1920	-2000	-1952	-1968	-1984	-1872	-1984	-1888	-1904	-1888	-1904	-1936	-1984	-1936	-1984	-1968	-1904	-1936	-1840	-1984	-1904	-1904	-1968	-1824	-1984	-1856	-1840	-1840	-1952	-1968
+-1744	-1696	-1824	-1744	-1760	-1808	-1632	-1808	-1680	-1696	-1664	-1680	-1744	-1792	-1712	-1792	-1792	-1664	-1744	-1616	-1792	-1680	-1664	-1760	-1584	-1824	-1632	-1600	-1600	-1728	-1760
+-1488	-1440	-1568	-1488	-1504	-1552	-1328	-1568	-1424	-1408	-1376	-1408	-1472	-1552	-1456	-1552	-1552	-1376	-1488	-1296	-1520	-1408	-1376	-1504	-1264	-1568	-1312	-1264	-1280	-1456	-1520
+-960	-768	-1200	-960	-1008	-1152	-400	-1216	-672	-688	-592	-656	-864	-1168	-880	-1168	-1168	-592	-944	-320	-1104	-672	-592	-1008	-192	-1200	-352	-208	-272	-848	-1040
+416	656	-16	400	320	112	1040	-48	800	768	864	816	544	64	528	48	48	864	432	1104	176	784	832	336	1216	-16	1088	1216	1152	544	272
+1568	1696	1328	1584	1536	1408	1824	1296	1744	1728	1760	1744	1632	1376	1632	1376	1376	1760	1600	1824	1456	1744	1744	1552	1856	1344	1824	1856	1856	1648	1504
+1904	1888	1872	1888	1872	1888	1840	1856	1872	1888	1872	1888	1904	1872	1888	1888	1888	1888	1888	1856	1888	1888	1872	1888	1840	1872	1872	1840	1840	1888	1888
+1744	1680	1808	1744	1760	1792	1520	1824	1616	1648	1616	1632	1712	1808	1712	1808	1808	1600	1744	1488	1792	1648	1600	1760	1408	1808	1488	1408	1440	1712	1776
+1008	752	1296	960	1024	1216	304	1312	592	624	512	592	864	1232	864	1264	1264	528	976	224	1168	608	544	1024	96	1296	272	112	176	848	1088
+-384	-592	-48	-432	-384	-160	-848	-16	-704	-704	-768	-720	-528	-144	-528	-96	-112	-752	-448	-864	-240	-720	-736	-384	-896	-48	-848	-880	-880	-528	-304
+-784	-688	-912	-832	-848	-912	-464	-912	-640	-672	-592	-640	-784	-896	-784	-912	-912	-592	-816	-400	-896	-656	-608	-864	-288	-912	-416	-304	-352	-768	-880
+176	352	-160	160	96	-80	624	-208	448	416	480	448	256	-112	240	-128	-112	496	160	672	-16	432	480	112	752	-176	656	752	720	256	48
+1008	1088	832	1008	992	896	1168	816	1120	1120	1120	1120	1056	880	1056	864	864	1136	1008	1184	928	1120	1136	992	1200	848	1168	1200	1184	1072	976
+1216	1216	1200	1232	1232	1216	1200	1216	1216	1216	1216	1216	1216	1216	1232	1216	1216	1216	1232	1184	1216	1216	1216	1232	1168	1200	1200	1168	1200	1216	1216
+1056	1024	1136	1088	1120	1136	912	1152	992	992	976	992	1056	1152	1072	1152	1136	976	1088	880	1120	992	976	1104	832	1152	896	816	848	1056	1120
+480	336	752	544	592	704	64	800	256	288	224	256	448	720	464	736	704	208	528	-16	672	272	224	576	-160	768	-16	-160	-96	416	608
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+-1616	-1696	-1392	-1584	-1552	-1440	-1792	-1344	-1712	-1728	-1744	-1728	-1648	-1424	-1648	-1424	-1408	-1760	-1600	-1808	-1488	-1728	-1744	-1568	-1824	-1392	-1792	-1840	-1808	-1664	-1536
+-1872	-1856	-1856	-1856	-1856	-1872	-1840	-1840	-1856	-1856	-1840	-1840	-1872	-1840	-1872	-1840	-1840	-1840	-1872	-1824	-1856	-1856	-1856	-1856	-1824	-1856	-1840	-1840	-1824	-1856	-1856
+-1776	-1744	-1824	-1792	-1792	-1808	-1712	-1824	-1744	-1728	-1728	-1744	-1760	-1808	-1776	-1808	-1824	-1728	-1776	-1696	-1808	-1728	-1728	-1776	-1680	-1824	-1696	-1664	-1680	-1760	-1792
+-1568	-1552	-1648	-1600	-1584	-1632	-1488	-1648	-1536	-1536	-1504	-1520	-1552	-1632	-1568	-1632	-1648	-1520	-1584	-1472	-1616	-1520	-1504	-1584	-1440	-1648	-1472	-1456	-1456	-1568	-1600
+-1360	-1312	-1424	-1376	-1392	-1408	-1280	-1440	-1328	-1328	-1312	-1312	-1328	-1408	-1344	-1424	-1408	-1312	-1376	-1264	-1408	-1312	-1296	-1376	-1232	-1424	-1280	-1248	-1248	-1344	-1392
+-1168	-1120	-1216	-1184	-1168	-1200	-1072	-1232	-1104	-1104	-1104	-1104	-1136	-1200	-1152	-1232	-1216	-1088	-1152	-1056	-1184	-1104	-1104	-1168	-1040	-1216	-1056	-1040	-1040	-1136	-1184
+-960	-928	-1024	-960	-976	-1008	-896	-1024	-912	-912	-912	-912	-944	-992	-944	-1024	-1008	-896	-944	-864	-992	-896	-896	-976	-848	-1008	-880	-832	-848	-944	-976
+-784	-768	-832	-784	-800	-816	-704	-832	-736	-768	-720	-736	-768	-800	-768	-832	-832	-720	-784	-704	-800	-736	-736	-800	-688	-832	-688	-672	-688	-768	-800
+-624	-608	-672	-624	-640	-656	-560	-688	-592	-592	-576	-576	-608	-656	-608	-656	-656	-576	-624	-560	-656	-592	-592	-640	-544	-672	-560	-544	-528	-624	-640
+-496	-480	-544	-512	-512	-528	-464	-544	-480	-480	-464	-464	-480	-512	-496	-528	-512	-464	-496	-464	-512	-480	-464	-512	-432	-528	-448	-448	-448	-480	-512
+-400	-384	-432	-416	-400	-416	-368	-432	-384	-384	-384	-384	-400	-416	-400	-432	-432	-368	-400	-352	-432	-384	-384	-416	-336	-432	-368	-352	-352	-384	-400
+-336	-320	-368	-320	-336	-352	-304	-352	-304	-304	-304	-304	-336	-336	-320	-336	-352	-304	-320	-288	-336	-304	-320	-320	-288	-352	-304	-288	-288	-320	-336
+-256	-240	-272	-256	-272	-272	-240	-272	-240	-240	-224	-256	-272	-272	-272	-272	-288	-240	-256	-240	-272	-256	-240	-272	-224	-272	-240	-224	-224	-256	-272
+-208	-192	-224	-176	-208	-224	-176	-224	-192	-192	-192	-176	-176	-224	-192	-208	-224	-176	-208	-176	-208	-176	-176	-192	-176	-224	-176	-160	-176	-192	-208
+-144	-128	-144	-144	-144	-176	-112	-176	-112	-112	-112	-128	-128	-160	-144	-160	-160	-112	-144	-112	-160	-112	-128	-144	-112	-160	-112	-96	-112	-128	-144
+-80	-80	-96	-80	-80	-112	-48	-96	-48	-48	-64	-64	-64	-96	-64	-96	-96	-64	-80	-48	-96	-48	-48	-80	-32	-112	-48	-32	-32	-64	-80
+-16	0	-32	-16	-16	-32	16	-16	16	0	0	16	0	-32	0	-16	-32	16	-32	16	-16	0	16	0	32	-16	32	16	32	-16	-16
+64	64	32	48	64	32	80	32	64	64	64	64	48	32	64	32	48	64	48	80	48	48	64	64	64	32	64	80	80	32	48
+96	112	80	96	96	96	112	96	112	128	112	128	112	96	96	96	96	112	96	112	96	112	112	96	112	80	112	112	112	112	80
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+160	160	160	160	160	160	160	144	160	160	176	160	160	160	160	144	160	160	160	176	160	160	160	144	160	160	160	160	176	160	160
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+176	160	176	160	160	160	160	160	160	160	160	160	160	176	176	176	176	160	160	160	176	176	160	176	160	160	176	160	160	176	176
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+128	-832	-64	160	512	544	640	336	384	400	416	368	256	-32	224	-16	384	384	336	416	320	128	-32	-320	-816	-352	-528	-400	192	256	496
+144	-1040	-128	96	512	608	608	480	496	544	576	464	320	-80	272	-80	384	480	416	416	384	256	32	-496	-736	-384	-208	32	464	464	576
+112	-816	-64	-48	416	560	416	496	448	576	576	416	288	-48	304	-16	352	432	368	256	368	256	16	-384	-336	-128	240	384	544	528	512
+0	-288	64	-192	112	368	-16	368	272	464	416	176	112	0	272	48	272	240	80	-208	160	48	-128	-112	160	224	512	528	448	416	304
+-96	272	176	-256	-352	-96	-576	-16	-96	144	16	-256	-176	0	144	64	48	-192	-400	-784	-240	-320	-400	160	496	416	544	448	144	64	-176
+-80	608	272	-160	-672	-640	-880	-528	-496	-320	-432	-640	-400	-16	-80	-48	-272	-704	-832	-1184	-736	-656	-688	272	576	448	400	176	-320	-368	-720
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diff --git a/testEssayScriptExample.c b/testEssayScriptExample.c
new file mode 100644
index 0000000..b8d741e
--- /dev/null
+++ b/testEssayScriptExample.c
@@ -0,0 +1,2200 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <string.h>
+#include <float.h>
+#include <windows.h>
+#include <time.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <stdint.h>
+#include <math.h>
+#include <complex.h>
+int nextpow2(int);
+double sinc(double);
+
+
+#pragma pack(push, 1)
+typedef struct {
+	uint16_t type;
+	uint32_t size;
+	uint16_t reserved1;
+	uint16_t reserved2;
+	uint32_t offset;
+	uint32_t dib_header_size;
+	int32_t width_px;
+	int32_t height_px;
+	uint16_t num_planes;
+	uint16_t bits_per_pixel;
+	uint32_t compression;
+	uint32_t image_size_bytes;
+	int32_t x_resolution_ppm;
+	int32_t y_resolution_ppm;
+	uint32_t num_colors;
+	uint32_t important_colors;
+} BMPHeader;
+#pragma pack(pop)
+
+void write_bmp_header(FILE* file, int width, int height) {
+	BMPHeader header = { 0 };
+	int row_padded = (width * 3 + 3) & (~3);
+	int data_size = row_padded * height;
+	int file_size = 54 + data_size;
+
+	header.type = 0x4D42;
+	header.size = file_size;
+	header.offset = 54;
+	header.dib_header_size = 40;
+	header.width_px = width;
+	header.height_px = height;
+	header.num_planes = 1;
+	header.bits_per_pixel = 24;
+	header.image_size_bytes = data_size;
+
+	fwrite(&header, sizeof(BMPHeader), 1, file);
+}
+
+void save_matrix_as_bmp(double** matrix, int width, int height, const char* filename) {
+	FILE* file = fopen(filename, "wb");
+	if (!file) {
+		fprintf(stderr, "Impossible d'ouvrir le fichier %s\n", filename);
+		return;
+	}
+
+	write_bmp_header(file, width, height);
+
+	int row_padded = (width * 3 + 3) & (~3);
+	uint8_t padding[3] = { 0, 0, 0 };
+	int padding_size = row_padded - (width * 3);
+
+	// Trouver les valeurs min et max dans la matrice pour la normalisation
+	double min_val = matrix[0][0];
+	double max_val = matrix[0][0];
+	for (int y = 0; y < height; y++) {
+		for (int x = 0; x < width; x++) {
+			if (matrix[y][x] < min_val) min_val = matrix[y][x];
+			if (matrix[y][x] > max_val) max_val = matrix[y][x];
+		}
+	}
+
+	for (int y = height - 1; y >= 0; y--) {
+		for (int x = 0; x < width; x++) {
+			// Normaliser et convertir en uint8_t
+			uint8_t pixel = (uint8_t)(255 * (matrix[y][x] - min_val) / (max_val - min_val));
+			uint8_t color[3] = { pixel, pixel, pixel };
+			fwrite(color, 3, 1, file);
+		}
+		fwrite(padding, padding_size, 1, file);
+	}
+
+	fclose(file);
+}
+
+
+
+
+#define pi 3.1416
+#define eps 2.2204e-16
+#define _CRT_SECURE_NO_WARNINGS 
+#define DATA_DIR L"C:\\Users\\yazan\\Desktop\\07_07_2024\\Stage ijl\\UTSR_CPP\\EssayScriptExample\\AcquiredData\\Specimen01\\*"
+#define MAX_FILENAME_LEN 256
+#define MAX_DATA_LEN 10000
+
+
+void main()
+{
+	printf("**************** run main ********************* \n");
+	// Defines essay parameters
+	// Propagation medium and transducer parameters
+	double TendGate, cl, d, fc, bw, A0, alpha_atenu, T1;
+	TendGate = 24.98; cl = 5859.4; d = 6.35;
+	fc = 4.6; bw = 4.4; A0 = 2.02;
+	alpha_atenu = 0.03548; T1 = 100e-9;
+	// Generating a infinitesimal point discontinuity model for calibration
+	// ROI(in mm)
+	double minX, maxX, minZ, maxZ, DepthCentre;
+	minX = 0; maxX = 30;
+	minZ = 40; maxZ = 41.7;
+	DepthCentre = 40;
+	//simulNDT
+	double deltaT_simul;
+	int TsGate_simul, AscanPoints_simul, Rows_simul, Diameter_simul;
+	deltaT_simul = 0.02;
+	TsGate_simul = 0;
+	AscanPoints_simul = (int)(TendGate / deltaT_simul) + 1;
+	Rows_simul = (int)(maxX)+1;
+	Diameter_simul = 0;
+	double** timeScale_simul = (double**)malloc(AscanPoints_simul * sizeof(double*));
+	int** X_simul = (int**)malloc(Rows_simul * sizeof(int*));
+	for (int i = 0; i < AscanPoints_simul; i++)
+	{
+		timeScale_simul[i] = (double*)malloc(1 * sizeof(double));
+		timeScale_simul[i][0] = i * deltaT_simul;
+	}
+	for (int i = 0; i < Rows_simul; i++)
+	{
+		X_simul[i] = (int*)malloc(1 * sizeof(int));
+		X_simul[i][0] = i;
+	}
+	// Getting calibration data
+	double ERMv, du;
+	ERMv = cl / 2;
+	du = (X_simul[1][0] - X_simul[0][0]) * 1e-3;
+	// GenerateModelFilter
+	double deltaScanX_g, deltaT_g, y_g;
+	int Rx_g, nt0_g, nu0_g, nt_g, nu_g;
+	double** scanX_g = (double**)malloc(Rows_simul * sizeof(double*));
+
+	Rx_g = 1;
+	for (int i = 0; i < Rows_simul; i++)
+	{
+		scanX_g[i] = (double*)malloc(1 * sizeof(double));
+		scanX_g[i][0] = X_simul[i][0] * 1e-3;
+	}
+	deltaScanX_g = (scanX_g[1][0] - scanX_g[0][0]) / Rx_g;
+	deltaT_g = (timeScale_simul[1][0] - timeScale_simul[0][0]) * 1e-6;
+	nt0_g = AscanPoints_simul;
+	nu0_g = Rows_simul;
+	nu0_g = (nu0_g - 1) * Rx_g + 1;
+	nt_g = pow(2, nextpow2(nt0_g) + 1);
+	nu_g = 2 * nu0_g;
+
+	double** f_g = (double**)malloc(((double)nt_g) * sizeof(double*));
+	double** kx_g = (double**)malloc(((double)nu_g) * sizeof(double*));
+
+	for (int i = 0; i < nt_g; i++)
+	{
+		f_g[i] = (double*)malloc(1 * sizeof(double));
+		f_g[i][0] = (((-nt_g / 2) + i) / deltaT_g) / nt_g;
+	}
+	for (int i = 0; i < nu_g; i++)
+	{
+		kx_g[i] = (double*)malloc(1 * sizeof(double));
+		kx_g[i][0] = (((-nu_g / 2) + i) / deltaScanX_g) / nu_g;
+	}
+	// meshgrid(kx_g, f_g)
+	double** gf = (double**)malloc(((double)nt_g) * sizeof(double*));
+	double** gkx = (double**)malloc(((double)nt_g) * sizeof(double*));
+	for (int i = 0; i < nt_g; i++)
+	{
+		gf[i] = (double*)malloc(((double)nu_g) * sizeof(double));
+		gkx[i] = (double*)malloc(((double)nu_g) * sizeof(double));
+		for (int j = 0; j < nu_g; j++)
+		{
+			gf[i][j] = f_g[i][0];
+			gkx[i][j] = kx_g[j][0];
+		}
+	}// fin meshgrid(kx_g, f_g)
+	double gst;
+	int** mask_g = (int**)malloc(nt_g * sizeof(int*));
+
+	for (int i = 0; i < nt_g; i++)
+	{
+		mask_g[i] = (int*)malloc(nu_g * sizeof(int*));
+		for (int j = 0; j < nu_g; j++)
+		{
+			gst = gkx[i][j] / (gf[i][j] / ERMv);
+
+			if (fabs(gst) <= 1.0)
+			{
+				mask_g[i][j] = 1;
+			}
+			else
+			{
+				mask_g[i][j] = 0;
+			}
+		}
+	}
+	//jinc
+	double** C1 = (double**)malloc(((double)nt_g) * sizeof(double*));
+	//C1
+	for (int i = 0; i < nt_g; i++)
+	{
+		C1[i] = (double*)malloc(((double)nu_g) * sizeof(double));
+		for (int j = 0; j < nu_g; j++)
+		{
+			y_g = (_j1(((pi * gkx[i][j]) * ((d * 1e-3) / 2))) / (((pi * gkx[i][j]) * ((d * 1e-3) / 2))));
+			if (isnan(y_g))
+			{
+				y_g = 0.5;
+			}
+			C1[i][j] = ((y_g * y_g) * mask_g[i][j]) * ((pi / 2) * ((2 * (d * 1e-3 / 2) * (d * 1e-3 / 2) * (2 * pi) / ERMv) * fabs(f_g[i][0])));
+		}
+	}// fin jinc
+
+	// cossquare
+	double** Hed_r = (double**)malloc(((double)nt_g) * sizeof(double*));
+	double** Hed_i = (double**)malloc(((double)nt_g) * sizeof(double*));
+	double f1_g, f4_g, ss_g, ff1_g, ff2_g, ri1_g, ri2_g, r1_g, r2_g, r_g, ExcTransd_r, ExcTransd_i;
+	f1_g = (fc * 1e6) - (bw * 1e6);
+	f4_g = (fc * 1e6) + (bw * 1e6);
+	//Hed
+	for (int i = 0; i < nt_g; i++)
+	{
+		Hed_r[i] = (double*)malloc(1 * sizeof(double));
+		Hed_i[i] = (double*)malloc(1 * sizeof(double));
+		ss_g = sin(pi * f_g[i][0] / (2 * (fc * 1e6)));
+		ri1_g = (fabs(f_g[i][0]) > (fc * 1e6)) && (fabs(f_g[i][0]) <= f4_g);
+		ri2_g = (fabs(f_g[i][0]) <= (fc * 1e6)) && (fabs(f_g[i][0]) <= f4_g);
+		ff1_g = ri1_g * fabs(f_g[i][0]);
+		ff2_g = ri2_g * fabs(f_g[i][0]);
+		r1_g = ri1_g * (cos(pi * ((fc * 1e6) - ff1_g) / (f4_g - f1_g)) * cos(pi * ((fc * 1e6) - ff1_g) / (f4_g - f1_g)));
+		r2_g = ri2_g * ss_g * (cos(pi * ((fc * 1e6) - ff2_g) / (f4_g - f1_g)) * cos(pi * ((fc * 1e6) - ff2_g) / (f4_g - f1_g)));
+		if (f_g[i][0] == 0)
+		{
+			r_g = r1_g;
+		}
+		else
+		{
+			r_g = r1_g + copysign(1.0, f_g[i][0] == 0) * r2_g;
+		}
+		ExcTransd_r = 2 * pi * sinc((2 * pi * f_g[i][0] * (T1 / 2))) * (-cos(-2 * pi * f_g[i][0] * (T1 / 2)));
+		ExcTransd_i = 2 * pi * sinc((2 * pi * f_g[i][0] * (T1 / 2))) * (-sin(-2 * pi * f_g[i][0] * (T1 / 2)));
+
+		if (fabs(f_g[i][0]) <= 10e6)
+		{
+			Hed_r[i][0] = 1.5 * pi * r_g * r_g * ExcTransd_r;
+			Hed_i[i][0] = 1.5 * pi * r_g * r_g * ExcTransd_i;
+		}
+		else
+		{
+			Hed_r[i][0] = 0.0;
+			Hed_i[i][0] = 0.0;
+		}
+	}//
+
+	double** Model_r = (double**)malloc(((double)nt_g) * sizeof(double*));
+	double** Model_i = (double**)malloc(((double)nt_g) * sizeof(double*));
+	double** Filt_r = (double**)malloc(((double)nt_g) * sizeof(double*));
+	double** Filt_i = (double**)malloc(((double)nt_g) * sizeof(double*));
+	for (int i = 0; i < nt_g; i++)
+	{
+		Model_r[i] = (double*)malloc(((double)nu_g) * sizeof(double));
+		Model_i[i] = (double*)malloc(((double)nu_g) * sizeof(double));
+		Filt_r[i] = (double*)malloc(((double)nu_g) * sizeof(double));
+		Filt_i[i] = (double*)malloc(((double)nu_g) * sizeof(double));
+
+		for (int j = 0; j < nu_g; j++)
+		{
+			Model_r[i][j] = C1[i][j] * Hed_r[i][0];
+			Model_i[i][j] = C1[i][j] * Hed_i[i][0];
+			//conj(model)
+			Filt_r[i][j] = C1[i][j] * Hed_r[i][0];
+			Filt_i[i][j] = -C1[i][j] * Hed_i[i][0];
+		}
+	}
+	/* save_matrix_as_bmp(Model_i, nu_g, nt_g, "module.bmp");
+	 const char* filename1 = "module.bmp";
+	 #ifdef _WIN32
+		 system("start module.bmp");
+	 #elif __APPLE__
+		 system("open module.bmp");
+	 #elif __linux__
+		 system("xdg-open module.bmp");
+	 #else
+		 printf("Image sauvegardée sous %s\n", filename1);
+	 #endif*/
+
+	 // fin GenerateModelFilter
+	free(timeScale_simul); free(X_simul);
+	free(scanX_g); free(f_g);
+	free(kx_g); free(gf);
+	free(gkx); free(mask_g); free(C1);
+	free(Hed_r); free(Hed_i);
+	//Defines regularization parameter
+	double alpha = 0.02;
+	// Loading acquired data
+	FILE* file = fopen("AscanValuesL.txt", "r");
+	if (file == NULL) {
+		perror("Erreur lors de l'ouverture du fichier");
+		return 1;
+	}
+	int rows = 0;
+	int cols = 0;
+	int temp;
+	char line[1024];
+	while (fgets(line, sizeof(line), file)) {
+		cols = 0;
+		char* ptr = line;
+		while (sscanf_s(ptr, "%d", &temp) == 1) {
+			cols++;
+			while (*ptr != '\0' && *ptr != ' ' && *ptr != '\t') ptr++;
+			while (*ptr == ' ' || *ptr == '\t') ptr++;
+		}
+		rows++;
+	}
+	// printf("rows=%d,cols=%d\n", rows, cols);
+	double** AscanValues_ptAco40dB = (double**)malloc(((double)rows) * sizeof(double*));
+	for (int i = 0; i < rows; i++) {
+		AscanValues_ptAco40dB[i] = (double*)malloc(((double)cols) * sizeof(double));
+	}
+	rewind(file);
+	int i = 0, j = 0;
+	while (fgets(line, sizeof(line), file)) {
+		j = 0;
+		char* ptr = line;
+		while (sscanf_s(ptr, "%d", &temp) == 1) {
+			AscanValues_ptAco40dB[i][j++] = (double)temp * (double)((0.5 / 2048) / 100);
+			while (*ptr != '\0' && *ptr != ' ' && *ptr != '\t') ptr++;
+			while (*ptr == ' ' || *ptr == '\t') ptr++;
+		}
+		i++;
+	}
+	fclose(file);
+
+	double deltaT_Load, sum_Load;
+	int backDepth_Load, Frequency_ptAco40dB;
+	double Cl_ptAco40dB, ProbeDiameter_ptAco40dB, Wavelength_ptAco40dB;
+	int backWallIdx[1][2] = { 1029,1029 };
+	deltaT_Load = 0.02;
+	backDepth_Load = 60;
+
+	double** timeScale_ptAco40dB = (double**)malloc((rows) * sizeof(double*));
+
+	for (int i = 0; i < rows; i++)
+	{
+		timeScale_ptAco40dB[i] = (double*)malloc(1 * sizeof(double));
+		timeScale_ptAco40dB[i][0] = deltaT_Load * i;
+	}
+	double** X_ptAco40dB = (double**)malloc(((double)cols) * sizeof(double*));
+	for (int i = 0; i < cols; i++)
+	{
+		X_ptAco40dB[i] = (double*)malloc(1 * sizeof(double));
+		X_ptAco40dB[i][0] = i;
+	}
+	sum_Load = 0;
+	for (int i = 0; i < 2; i++)
+	{
+		int var_x = backWallIdx[0][i] - 1;
+		sum_Load = sum_Load + ((backDepth_Load * 2000) / (timeScale_ptAco40dB[var_x][0]));
+	}
+	Cl_ptAco40dB = sum_Load / 2;
+	Frequency_ptAco40dB = 5;
+	ProbeDiameter_ptAco40dB = 6.35;
+	Wavelength_ptAco40dB = Cl_ptAco40dB / (Frequency_ptAco40dB * 1000);
+	double** zz_Load = (double**)malloc((rows) * sizeof(double*));
+	double** ffc_Load = (double**)malloc((rows) * sizeof(double*));
+	double var_x1 = 0;
+	for (int i = 0; i < rows; i++)
+	{
+		zz_Load[i] = (double*)malloc(1 * sizeof(double));
+		ffc_Load[i] = (double*)malloc(1 * sizeof(double));
+		zz_Load[i][0] = (timeScale_ptAco40dB[i][0] * Cl_ptAco40dB) / 2000;
+		var_x1 = (1 / A0) * exp(alpha_atenu * zz_Load[i][0]);
+		if (var_x1 < 1)
+		{
+			ffc_Load[i][0] = 1;
+		}
+		else
+		{
+			ffc_Load[i][0] = var_x1;
+		}
+	}
+	for (int i = 0; i < rows; i++)
+	{
+		for (int j = 0; j < cols; j++)
+		{
+			AscanValues_ptAco40dB[i][j] = AscanValues_ptAco40dB[i][j] * ffc_Load[i][0];
+		}
+	}
+	//    save_matrix_as_bmp(AscanValues_ptAco40dB, cols, rows, "AscanValues_ptAco40dB.bmp");
+	//    const char* filename2 = "AscanValues_ptAco40dB.bmp";
+	//#ifdef _WIN32
+	//    system("start AscanValues_ptAco40dB.bmp");
+	//#elif __APPLE__
+	//    system("open AscanValues_ptAco40dB.bmp");
+	//#elif __linux__
+	//    system("xdg-open AscanValues_ptAco40dB.bmp");
+	//#else
+	//    printf("Image sauvegardée sous %s\n", filename2);
+	//#endif
+
+		/// UTSR_ModS2
+	double ERMv1, scanY, deltaScanZ, apertAngle, tanApertAngle, limApertX, tau0, dt, beta, tol, cg_tol;
+	int idxMinZ, idxMaxZ, M, colIniX, Rx;
+	ERMv1 = Cl_ptAco40dB / 2;
+	double** scanX = (double**)malloc(((double)cols) * sizeof(double*));
+	for (int i = 0; i < cols; i++)
+	{
+		scanX[i] = (double*)malloc(1 * sizeof(double));
+		scanX[i][0] = X_ptAco40dB[i][0] * 1e-3;
+	}
+	double** scanZ = (double**)malloc((rows) * sizeof(double*));
+	for (int i = 0; i < rows; i++)
+	{
+		scanZ[i] = (double*)malloc(1 * sizeof(double));
+		scanZ[i][0] = timeScale_ptAco40dB[i][0] * 1e-6 * ERMv1;
+	}
+	deltaScanZ = scanZ[1][0] - scanZ[0][0];
+	apertAngle = asin((0.51 * Cl_ptAco40dB) / (Frequency_ptAco40dB * 1e6 * ProbeDiameter_ptAco40dB * 1e-3));
+	tanApertAngle = tan(apertAngle);
+	for (int i = 0; i < rows; i++)
+	{
+
+		if ((scanZ[i][0]) < ((double)(minZ * 1e-3)))
+		{
+			idxMinZ = i + 1;
+		}
+		if ((scanZ[i][0]) < ((double)(maxZ * 1e-3)))
+		{
+			idxMaxZ = i + 2;
+		}
+	}
+	M = (1 + (idxMaxZ - idxMinZ));
+	double** roiZ = (double**)malloc((double)M * sizeof(double*));
+	for (int i = 0; i < M; i++)
+	{
+		roiZ[i] = (double*)malloc(1 * sizeof(double));
+		roiZ[i][0] = scanZ[i + idxMinZ][0];
+	}
+	limApertX = roiZ[M - 1][0] * tanApertAngle;
+	for (int i = 0; i < cols; i++)
+	{
+		if ((scanX[i][0] + limApertX) >= scanX[0][0])
+		{
+			colIniX = i + 1;
+			break;
+		}
+	}
+	printf("$$$$$$$ Starting UTSR algorithm (alpha = %f) $$$$$$$\n", alpha);
+	printf("---- Title: UTSR solution ----\n");
+	clock_t tAlg = clock();
+	//----- Starting UTSR algorithm -----
+	double** S_t_u = (double**)malloc((double)M * sizeof(double*));
+	for (int i = 0; i < M; i++)
+	{
+		S_t_u[i] = (double*)malloc(cols * sizeof(double));
+		for (int j = 0; j < cols; j++)
+		{
+			S_t_u[i][j] = AscanValues_ptAco40dB[i + idxMinZ - 1][j];
+		}
+	}
+	//    save_matrix_as_bmp(S_t_u, cols, M, "S_t_u.bmp");
+	//    const char* filename3 = "S_t_u.bmp";
+	//#ifdef _WIN32
+	//    system("start S_t_u.bmp");
+	//#elif __APPLE__
+	//    system("open S_t_u.bmp");
+	//#elif __linux__
+	//    system("xdg-open S_t_u.bmp");
+	//#else
+	//    printf("Image sauvegardée sous %s\n", filename3);
+	//#endif
+	int fOrig = NULL;
+	tau0 = timeScale_ptAco40dB[idxMinZ - 1][0] * 1e-6;
+	int szData[1][2] = { M,cols };
+	dt = deltaScanZ / ERMv1;
+	beta = 1;
+	tol = 1e-2;
+	cg_tol = 1e-2;
+	Rx = 1;
+	// ModS2T(S_t_u, dt, dx, ERMv, tau0, Filt, Rx)
+	//meshgrid(ku,f)
+	printf("nt_g=%d, nu_g=%d, M=%d, cols=%d\n", nt_g, nu_g, M, cols);
+
+	double** f_ModS2T = (double**)malloc(nt_g * sizeof(double*));
+	double** ku_ModS2T = (double**)malloc(nt_g * sizeof(double*));
+	double** fkz_ModS2T = (double**)malloc(nt_g * sizeof(double*));
+	double sign_f;
+	for (int i = 0; i < nt_g; i++)
+	{
+		f_ModS2T[i] = (double*)malloc(nu_g * sizeof(double));
+		ku_ModS2T[i] = (double*)malloc(nu_g * sizeof(double));
+		fkz_ModS2T[i] = (double*)malloc(nu_g * sizeof(double));
+		for (int j = 0; j < nu_g; j++)
+		{
+			f_ModS2T[i][j] = (((double)(-nt_g / 2.0) + i) / dt) / nt_g;
+			ku_ModS2T[i][j] = (((double)(-nu_g / 2.0) + j) / du) / nu_g;
+			sign_f = (f_ModS2T[i][j] > 0) - (f_ModS2T[i][j] < 0);
+			fkz_ModS2T[i][j] = ERMv1 * sign_f * sqrt((ku_ModS2T[i][j] * ku_ModS2T[i][j]) + ((f_ModS2T[i][j] / ERMv1) * (f_ModS2T[i][j] / ERMv1)));
+			// printf("%e\t", f_ModS2T[i][j]);
+		}
+		// printf("\n");
+	}
+
+
+
+		// start timing for FFT
+	
+	// FFT2(S_t_u, nt_g, nu_g)
+	double sum_ftimage1_r_ModS2T = 0.0;
+	double sum_ftimage1_i_ModS2T = 0.0;
+	double** ftimage1_r_ModS2T = (double**)malloc(nt_g * sizeof(double*));
+	double** ftimage1_i_ModS2T = (double**)malloc(nt_g * sizeof(double*));
+	for (int k1 = 0; k1 < nt_g; k1++)
+	{
+		ftimage1_r_ModS2T[k1] = (double*)malloc(nu_g * sizeof(double));
+		ftimage1_i_ModS2T[k1] = (double*)malloc(nu_g * sizeof(double));
+		for (int k2 = 0; k2 < nu_g; k2++)
+		{
+			for (int n1 = 0; n1 < M; n1++)
+			{
+				for (int n2 = 0; n2 < cols; n2++)
+				{
+					double angle = 2 * pi * ((double)(k1 * n1) / nt_g + (double)(k2 * n2) / nu_g);
+					sum_ftimage1_r_ModS2T = sum_ftimage1_r_ModS2T + (S_t_u[n1][n2] * cos(angle));
+					sum_ftimage1_i_ModS2T = sum_ftimage1_i_ModS2T - S_t_u[n1][n2] * sin(angle);
+				}
+			}
+			ftimage1_r_ModS2T[k1][k2] = sum_ftimage1_r_ModS2T;
+			ftimage1_i_ModS2T[k1][k2] = sum_ftimage1_i_ModS2T;
+			sum_ftimage1_i_ModS2T = 0.0;
+			sum_ftimage1_r_ModS2T = 0.0;
+		}
+	}
+
+	//fftshift
+	double** ftimage21_r_ModS2T = (double**)malloc(nt_g * sizeof(double*));
+	double** ftimage21_i_ModS2T = (double**)malloc(nt_g * sizeof(double*));
+
+	int a_fftshift, b_fftshift;
+	if (nt_g % 2 == 0)
+	{
+		a_fftshift = 0;
+	}
+	else {
+		a_fftshift = 1;
+	}
+	if (nu_g % 2 == 0)
+	{
+		b_fftshift = 0;
+	}
+	else
+	{
+		b_fftshift = 1;
+	}
+	for (int i = 0; i < nt_g; i++)
+	{
+		ftimage21_r_ModS2T[i] = (double*)malloc(nu_g * sizeof(double));
+		ftimage21_i_ModS2T[i] = (double*)malloc(nu_g * sizeof(double));
+		for (int j = 0; j < nu_g; j++)
+		{
+
+			if (b_fftshift == 1)
+			{
+				if (j < (int)(nu_g / 2))
+				{
+					ftimage21_r_ModS2T[i][j] = ftimage1_r_ModS2T[i][j + (int)(nu_g / 2) + 1];
+					ftimage21_i_ModS2T[i][j] = ftimage1_i_ModS2T[i][j + (int)(nu_g / 2) + 1];
+				}
+				else
+				{
+					ftimage21_r_ModS2T[i][j] = ftimage1_r_ModS2T[i][j - (int)(nu_g / 2)];
+					ftimage21_i_ModS2T[i][j] = ftimage1_i_ModS2T[i][j - (int)(nu_g / 2)];
+				}
+			}
+			if (b_fftshift == 0)
+			{
+				if (j < (int)(nu_g / 2))
+				{
+					ftimage21_r_ModS2T[i][j] = ftimage1_r_ModS2T[i][j + (int)(nu_g / 2)];
+					ftimage21_i_ModS2T[i][j] = ftimage1_i_ModS2T[i][j + (int)(nu_g / 2)];
+				}
+				else
+				{
+					ftimage21_r_ModS2T[i][j] = ftimage1_r_ModS2T[i][j - (int)(nu_g / 2)];
+					ftimage21_i_ModS2T[i][j] = ftimage1_i_ModS2T[i][j - (int)(nu_g / 2)];
+				}
+			}
+		}
+	}
+
+	double** ftimage2_r_ModS2T = (double**)malloc(nt_g * sizeof(double*));
+	double** ftimage2_i_ModS2T = (double**)malloc(nt_g * sizeof(double*));
+	for (int i = 0; i < nt_g; i++)
+	{
+		ftimage2_r_ModS2T[i] = (double*)malloc(nu_g * sizeof(double));
+		ftimage2_i_ModS2T[i] = (double*)malloc(nu_g * sizeof(double));
+		for (int j = 0; j < nu_g; j++)
+		{
+			if (a_fftshift == 1)
+			{
+				if (i < (nt_g / 2))
+				{
+
+					ftimage2_r_ModS2T[i][j] = ftimage21_r_ModS2T[i + (int)(nt_g / 2) + 1][j];
+					ftimage2_i_ModS2T[i][j] = ftimage21_i_ModS2T[i + (int)(nt_g / 2) + 1][j];
+				}
+				else
+				{
+					ftimage2_r_ModS2T[i][j] = ftimage21_r_ModS2T[i - (int)(nt_g / 2)][j];
+					ftimage2_i_ModS2T[i][j] = ftimage21_i_ModS2T[i - (int)(nt_g / 2)][j];
+				}
+			}
+			if (a_fftshift == 0)
+			{
+				if (i < (nt_g / 2))
+				{
+					ftimage2_r_ModS2T[i][j] = ftimage21_r_ModS2T[i + (int)(nt_g / 2)][j];
+					ftimage2_i_ModS2T[i][j] = ftimage21_i_ModS2T[i + (int)(nt_g / 2)][j];
+				}
+				else
+				{
+					ftimage2_r_ModS2T[i][j] = ftimage21_r_ModS2T[i - (int)(nt_g / 2)][j];
+					ftimage2_i_ModS2T[i][j] = ftimage21_i_ModS2T[i - (int)(nt_g / 2)][j];
+				}
+			}
+			// printf("%f  ", ftimage2_r_ModS2T[i][j]);
+		}
+		//printf("\n");
+	}
+
+
+
+
+
+	free(ftimage21_r_ModS2T); free(ftimage21_i_ModS2T);
+	free(ftimage1_r_ModS2T); free(ftimage1_i_ModS2T);
+	printf("fin fftshift\n");
+	// tau0
+	double** ftimage_r_ModS2T = (double**)malloc(nt_g * sizeof(double*));
+	double** ftimage_i_ModS2T = (double**)malloc(nt_g * sizeof(double*));
+	for (int i = 0; i < nt_g; i++)
+	{
+		ftimage_r_ModS2T[i] = (double*)malloc(nu_g * sizeof(double));
+		ftimage_i_ModS2T[i] = (double*)malloc(nu_g * sizeof(double));
+		for (int j = 0; j < nu_g; j++)
+		{
+			//teste
+			double angle = 2 * pi * (double)(fkz_ModS2T[i][j] - f_ModS2T[i][j]) * tau0;
+			double angcos = cos(angle);
+			double angsin = -sin(angle);
+			double re = ftimage2_r_ModS2T[i][j] * angcos - ftimage2_i_ModS2T[i][j] * angsin;
+			double im = ftimage2_i_ModS2T[i][j] * angcos + ftimage2_r_ModS2T[i][j] * angsin;
+			ftimage_r_ModS2T[i][j] = re * Filt_r[i][j] - im * Filt_i[i][j];
+			ftimage_i_ModS2T[i][j] = re * Filt_i[i][j] + im * Filt_r[i][j];
+			//printf("%e\t", ftimage_i_ModS2T[i][j]);
+		}
+		//printf("\n");
+
+	}
+	printf("fin tau0\n");
+	free(ftimage2_r_ModS2T); free(ftimage2_i_ModS2T);
+	
+	//linterp  
+	double** Vq_linterp_r_ModS2T = (double**)malloc(nt_g * sizeof(double*));
+	double** Vq_linterp_i_ModS2T = (double**)malloc(nt_g * sizeof(double*));
+
+	for (int i = 0; i < nt_g; i++)
+	{
+		Vq_linterp_r_ModS2T[i] = (double*)malloc(nu_g * sizeof(double));
+		Vq_linterp_i_ModS2T[i] = (double*)malloc(nu_g * sizeof(double));
+		for (int j = 0; j < nu_g; j++)
+		{
+			Vq_linterp_r_ModS2T[i][j] = 0.0;
+			Vq_linterp_i_ModS2T[i][j] = 0.0;
+		}
+	}
+	double dx_linterp_ModS2T = f_ModS2T[1][0] - f_ModS2T[0][0];
+	for (int i = 0; i < nu_g; i++)
+	{
+		for (int j = 0; j < nt_g; j++)
+		{
+			double f1 = (fkz_ModS2T[j][i] - f_ModS2T[0][0]) / dx_linterp_ModS2T;
+			int fMask = !((fkz_ModS2T[j][i] < f_ModS2T[0][0]) | (fkz_ModS2T[j][i] > f_ModS2T[(nt_g - 1)][0]));
+			double f = f1 * fMask;
+			int im = (int)floor(f);
+			int im2Inval = (im + 2 > nt_g - 1) ? 1 : 0;
+
+			double fx = f - (double)im;
+			double gx = 1.0 - fx;
+			if (fMask == 1)
+			{
+				if (im2Inval > 0)
+				{
+					Vq_linterp_r_ModS2T[j][i] = gx * ftimage_r_ModS2T[im][i];
+					// printf("0\t");
+					Vq_linterp_i_ModS2T[j][i] = gx * ftimage_i_ModS2T[im][i];
+
+				}
+				else
+				{
+					Vq_linterp_r_ModS2T[j][i] = gx * ftimage_r_ModS2T[im][i] + fx * ftimage_r_ModS2T[im + 1][i];
+					Vq_linterp_i_ModS2T[j][i] = gx * ftimage_i_ModS2T[im][i] + fx * ftimage_i_ModS2T[im + 1][i];
+					// printf("%e\t", ftimage_r_ModS2T[im+1][i]);
+				}
+			}
+
+		}
+		//printf("\n");
+	}// fin linterp
+
+	srand(time(NULL));
+	printf("fin linterp\n");
+	//ifftshift(ftimage)
+	double** vq_r_ModS2T = (double**)malloc(nt_g * sizeof(double*));
+	double** vq_i_ModS2T = (double**)malloc(nt_g * sizeof(double*));
+	for (int i = 0; i < nt_g; i++)
+	{
+		vq_r_ModS2T[i] = (double*)malloc(nu_g * sizeof(double));
+		vq_i_ModS2T[i] = (double*)malloc(nu_g * sizeof(double));
+		for (int j = 0; j < nu_g; j++)
+		{
+
+			if (b_fftshift == 1)
+			{
+				if (j <= (int)(nu_g / 2))
+				{
+					vq_r_ModS2T[i][j] = Vq_linterp_r_ModS2T[i][j + (int)(nu_g / 2)];
+					vq_i_ModS2T[i][j] = Vq_linterp_i_ModS2T[i][j + (int)(nu_g / 2)];
+				}
+				else
+				{
+					vq_r_ModS2T[i][j] = Vq_linterp_r_ModS2T[i][j - ((int)(nu_g / 2) + 1)];
+					vq_i_ModS2T[i][j] = Vq_linterp_i_ModS2T[i][j - ((int)(nu_g / 2) + 1)];
+				}
+			}
+			if (b_fftshift == 0)
+			{
+				if (j < (int)(nu_g / 2))
+				{
+					vq_r_ModS2T[i][j] = Vq_linterp_r_ModS2T[i][j + (int)(nu_g / 2)];
+					vq_i_ModS2T[i][j] = Vq_linterp_i_ModS2T[i][j + (int)(nu_g / 2)];
+				}
+				else
+				{
+					vq_r_ModS2T[i][j] = Vq_linterp_r_ModS2T[i][j - (int)(nu_g / 2)];
+					vq_i_ModS2T[i][j] = Vq_linterp_i_ModS2T[i][j - (int)(nu_g / 2)];
+				}
+			}
+			//printf("%e\t", vq_r_ModS2T[i][j]);
+			//printf("%e\t",vq_i_ModS2T[i][j]);
+
+		}
+		//printf("\n");
+	}
+	// printf("\n");
+
+	double** vq1_r_ModS2T = (double**)malloc(nt_g * sizeof(double*));
+	double** vq1_i_ModS2T = (double**)malloc(nt_g * sizeof(double*));
+	for (int i = 0; i < nt_g; i++)
+	{
+		vq1_r_ModS2T[i] = (double*)malloc(nu_g * sizeof(double));
+		vq1_i_ModS2T[i] = (double*)malloc(nu_g * sizeof(double));
+		for (int j = 0; j < nu_g; j++)
+		{
+
+			if (a_fftshift == 1)
+			{
+				if (i <= (nt_g / 2))
+				{
+
+					vq1_r_ModS2T[i][j] = vq_r_ModS2T[i + (int)(nt_g / 2)][j];
+					vq1_i_ModS2T[i][j] = vq_i_ModS2T[i + (int)(nt_g / 2)][j];
+				}
+				else
+				{
+					vq1_r_ModS2T[i][j] = vq_r_ModS2T[i - ((int)(nt_g / 2) + 1)][j];
+					vq1_i_ModS2T[i][j] = vq_i_ModS2T[i - ((int)(nt_g / 2) + 1)][j];
+				}
+			}
+			if (a_fftshift == 0)
+			{
+				if (i < (nt_g / 2))
+				{
+					vq1_r_ModS2T[i][j] = vq_r_ModS2T[i + (int)(nt_g / 2)][j];
+					vq1_i_ModS2T[i][j] = vq_i_ModS2T[i + (int)(nt_g / 2)][j];
+				}
+				else
+				{
+					vq1_r_ModS2T[i][j] = vq_r_ModS2T[i - (int)(nt_g / 2)][j];
+					vq1_i_ModS2T[i][j] = vq_i_ModS2T[i - (int)(nt_g / 2)][j];
+				}
+			}
+			//printf("%e\t", vq1_r_ModS2T[i][j]);
+			//printf("=%e\n", vq1_i_ModS2T[i][j]);
+		}
+		//printf("\n");
+	}
+
+	free(vq_r_ModS2T); free(vq_i_ModS2T);
+	free(Vq_linterp_r_ModS2T); free(Vq_linterp_i_ModS2T);
+	// fin nifftshift
+	printf("fin ifftshift\n");
+
+
+
+
+	// ifft
+	double** HTg_1 = (double**)malloc(M * sizeof(double*));
+	double cts_ifft = (nt_g * nu_g);
+	for (int n1 = 0; n1 < M; n1++)
+	{
+		HTg_1[n1] = (double*)malloc(cols * sizeof(double));
+		for (int n2 = 0; n2 < cols; n2++)
+		{
+			double som_r = 0.0;
+			for (int k1 = 0; k1 < nt_g; k1++)
+			{
+				for (int k2 = 0; k2 < nu_g; k2++)
+				{
+					double angle = 2.0 * pi * ((double)(k1 * n1) / nt_g + (double)(k2 * n2) / nu_g);
+					double cosangle = cos(angle);
+					double sinangle = sin(angle);
+					som_r = som_r + vq1_r_ModS2T[k1][k2] * cosangle - vq1_i_ModS2T[k1][k2] * sinangle;
+				}
+			}
+			HTg_1[n1][n2] = (som_r / cts_ifft);
+			//printf("%e\t", HTg_1[n1][n2]);
+
+		}
+		// printf("\n");
+	}// fin ifft
+	clock_t tEnd = clock();
+	double time_elapsed = ((double)(tEnd - tAlg)) / CLOCKS_PER_SEC;
+	printf("required time of IFFT is  : %f seconds.\n", time_elapsed);
+
+
+	    save_matrix_as_bmp(HTg_1, cols, M, "HTg_1.bmp");
+	    const char* filename4 = "HTg_1.bmp";
+	#ifdef _WIN32
+	    system("start HTg_1.bmp");
+	#elif __APPLE__
+	    system("open f_ModS2T.bmp");
+	#elif __linux__
+	    system("xdg-open f_ModS2T.bmp");
+	#else
+	    printf("Image sauvegardée sous %s\n", filename4);
+	#endif
+
+
+	double** HTg = (double**)malloc((M * cols) * sizeof(double*));
+	for (int i = 0; i < M; i++)
+	{
+		for (int j = 0; j < cols; j++)
+		{
+			HTg[((i * cols) + j)] = (double*)malloc(1 * sizeof(double));
+			HTg[((i * cols) + j)][0] = HTg_1[i][j] * Rx;
+		}
+	}
+	//free(HTg_1); 
+	free(f_ModS2T);
+	free(ku_ModS2T); free(fkz_ModS2T);
+	free(ftimage_r_ModS2T); free(ftimage_i_ModS2T);
+	// fin ModS2T
+	free(X_ptAco40dB); free(zz_Load);
+	free(ffc_Load); free(scanX);
+	free(scanZ); free(roiZ);
+	printf("fin ModS2T\n");
+	double** fTemp = (double**)malloc((M * cols) * sizeof(double*));
+	double** W = (double**)malloc((M * cols) * sizeof(double*));
+	double** Y_Model = (double**)malloc((M * cols) * sizeof(double*));
+	double** X_cg = (double**)malloc((M * cols) * sizeof(double*));
+	for (int i = 0; i < (M * cols); i++)
+	{
+		fTemp[i] = (double*)malloc(1 * sizeof(double));
+		X_cg[i] = (double*)malloc(1 * sizeof(double));
+		W[i] = (double*)malloc(1 * sizeof(double));
+		Y_Model[i] = (double*)malloc(1 * sizeof(double));
+		W[i][0] = 1.0;
+		fTemp[i][0] = 0.0; X_cg[i][0] = 0.01;
+		Y_Model[i][0] = 0.0;
+	}
+	// init varaible of model
+
+	double** res_x_szd = (double**)malloc(M * sizeof(double*));
+	double** g = (double**)malloc(M * sizeof(double*));
+	double** Y1_Model = (double**)malloc(M * sizeof(double*));
+	for (int i = 0; i < M; i++)
+	{
+		res_x_szd[i] = (double*)malloc(cols * sizeof(double));
+		g[i] = (double*)malloc(cols * sizeof(double));
+		Y1_Model[i] = (double*)malloc(cols * sizeof(double));
+		for (int j = 0; j < cols; j++)
+		{
+			res_x_szd[i][j] = 0.0;
+			g[i][j] = 0.0;
+			Y1_Model[i][j] = 0.0;
+		}
+
+	}
+
+	double** f_ModS2 = (double**)malloc(nt_g * sizeof(double*));
+	double** ku_ModS2 = (double**)malloc(nt_g * sizeof(double*));
+	double** fkz_ModS2 = (double**)malloc(nt_g * sizeof(double*));
+	double** ftimage1_r_ModS2 = (double**)malloc(nt_g * sizeof(double*));
+	double** ftimage1_i_ModS2 = (double**)malloc(nt_g * sizeof(double*));
+	double** ftimage21_r_ModS2 = (double**)malloc(nt_g * sizeof(double*));
+	double** ftimage21_i_ModS2 = (double**)malloc(nt_g * sizeof(double*));
+	double** ftimage2_r_ModS2 = (double**)malloc(nt_g * sizeof(double*));
+	double** ftimage2_i_ModS2 = (double**)malloc(nt_g * sizeof(double*));
+	double** V_linterpAdj_r_ModS2 = (double**)malloc(nt_g * sizeof(double*));
+	double** V_linterpAdj_i_ModS2 = (double**)malloc(nt_g * sizeof(double*));
+	double** pG_r_linterpAdj_ModS2 = (double**)malloc(nt_g * sizeof(double*));
+	double** pG_i_linterpAdj_ModS2 = (double**)malloc(nt_g * sizeof(double*));
+	double** pF_r_linterpAdj_ModS2 = (double**)malloc(nt_g * sizeof(double*));
+	double** pF_i_linterpAdj_ModS2 = (double**)malloc(nt_g * sizeof(double*));
+	double** ftimage_r_ModS2 = (double**)malloc(nt_g * sizeof(double*));
+	double** ftimage_i_ModS2 = (double**)malloc(nt_g * sizeof(double*));
+	double** ftdata_r_ModS2 = (double**)malloc(nt_g * sizeof(double*));
+	double** ftdata_i_ModS2 = (double**)malloc(nt_g * sizeof(double*));
+	double** ftdata1_r_ModS2 = (double**)malloc(nt_g * sizeof(double*));
+	double** ftdata1_i_ModS2 = (double**)malloc(nt_g * sizeof(double*));
+	double** f_model_ModS2T = (double**)malloc(nt_g * sizeof(double*));
+	double** ku_model_ModS2T = (double**)malloc(nt_g * sizeof(double*));
+	double** fkz_model_ModS2T = (double**)malloc(nt_g * sizeof(double*));
+	double** ftdata1_r_Model = (double**)malloc(nt_g * sizeof(double*));
+	double** ftdata1_i_Model = (double**)malloc(nt_g * sizeof(double*));
+	double** ftdata2_r_Model = (double**)malloc(nt_g * sizeof(double*));
+	double** ftdata2_i_Model = (double**)malloc(nt_g * sizeof(double*));
+	double** ftdata21_r_Model = (double**)malloc(nt_g * sizeof(double*));
+	double** ftdata21_i_Model = (double**)malloc(nt_g * sizeof(double*));
+	double** ftdata_r_Model = (double**)malloc(nt_g * sizeof(double*));
+	double** ftdata_i_Model = (double**)malloc(nt_g * sizeof(double*));
+	double** Vq1_linterp_r_Model = (double**)malloc(nt_g * sizeof(double*));
+	double** Vq1_linterp_i_Model = (double**)malloc(nt_g * sizeof(double*));
+	double** image1_r_Model = (double**)malloc(nt_g * sizeof(double*));
+	double** image1_i_Model = (double**)malloc(nt_g * sizeof(double*));
+	double** image2_r_Model = (double**)malloc(nt_g * sizeof(double*));
+	double** image2_i_Model = (double**)malloc(nt_g * sizeof(double*));
+
+	for (int i = 0; i < nt_g; i++)
+	{
+		f_ModS2[i] = (double*)malloc(nu_g * sizeof(double));
+		ku_ModS2[i] = (double*)malloc(nu_g * sizeof(double));
+		fkz_ModS2[i] = (double*)malloc(nu_g * sizeof(double));
+		ftimage1_r_ModS2[i] = (double*)malloc(nu_g * sizeof(double));
+		ftimage1_i_ModS2[i] = (double*)malloc(nu_g * sizeof(double));
+		ftimage21_r_ModS2[i] = (double*)malloc(nu_g * sizeof(double));
+		ftimage21_i_ModS2[i] = (double*)malloc(nu_g * sizeof(double));
+		ftimage2_r_ModS2[i] = (double*)malloc(nu_g * sizeof(double));
+		ftimage2_i_ModS2[i] = (double*)malloc(nu_g * sizeof(double));
+		V_linterpAdj_r_ModS2[i] = (double*)malloc(nu_g * sizeof(double));
+		V_linterpAdj_i_ModS2[i] = (double*)malloc(nu_g * sizeof(double));
+		pG_r_linterpAdj_ModS2[i] = (double*)malloc(1 * sizeof(double));
+		pG_i_linterpAdj_ModS2[i] = (double*)malloc(1 * sizeof(double));
+		pF_r_linterpAdj_ModS2[i] = (double*)malloc(1 * sizeof(double));
+		pF_i_linterpAdj_ModS2[i] = (double*)malloc(1 * sizeof(double));
+		ftimage_r_ModS2[i] = (double*)malloc(nu_g * sizeof(double));
+		ftimage_i_ModS2[i] = (double*)malloc(nu_g * sizeof(double));
+		ftdata_r_ModS2[i] = (double*)malloc(nu_g * sizeof(double));
+		ftdata_i_ModS2[i] = (double*)malloc(nu_g * sizeof(double));
+		ftdata1_r_ModS2[i] = (double*)malloc(nu_g * sizeof(double));
+		ftdata1_i_ModS2[i] = (double*)malloc(nu_g * sizeof(double));
+		f_model_ModS2T[i] = (double*)malloc(nu_g * sizeof(double));
+		ku_model_ModS2T[i] = (double*)malloc(nu_g * sizeof(double));
+		fkz_model_ModS2T[i] = (double*)malloc(nu_g * sizeof(double));
+		ftdata1_r_Model[i] = (double*)malloc(nu_g * sizeof(double));
+		ftdata1_i_Model[i] = (double*)malloc(nu_g * sizeof(double));
+		ftdata2_r_Model[i] = (double*)malloc(nu_g * sizeof(double));
+		ftdata2_i_Model[i] = (double*)malloc(nu_g * sizeof(double));
+		ftdata21_r_Model[i] = (double*)malloc(nu_g * sizeof(double));
+		ftdata21_i_Model[i] = (double*)malloc(nu_g * sizeof(double));
+		ftdata_r_Model[i] = (double*)malloc(nu_g * sizeof(double));
+		ftdata_i_Model[i] = (double*)malloc(nu_g * sizeof(double));
+		Vq1_linterp_r_Model[i] = (double*)malloc(nu_g * sizeof(double));
+		Vq1_linterp_i_Model[i] = (double*)malloc(nu_g * sizeof(double));
+		image1_r_Model[i] = (double*)malloc(nu_g * sizeof(double));
+		image1_i_Model[i] = (double*)malloc(nu_g * sizeof(double));
+		image2_r_Model[i] = (double*)malloc(nu_g * sizeof(double));
+		image2_i_Model[i] = (double*)malloc(nu_g * sizeof(double));
+		for (int j = 0; j < nu_g; j++)
+		{
+			f_ModS2[i][j] = 0.0;
+			ku_ModS2[i][j] = 0.0;
+			fkz_ModS2[i][j] = 0.0;
+			ftimage1_r_ModS2[i][j] = 0.0;
+			ftimage1_i_ModS2[i][j] = 0.0;
+			ftimage21_r_ModS2[i][j] = 0.0;
+			ftimage21_i_ModS2[i][j] = 0.0;
+			ftimage2_r_ModS2[i][j] = 0.0;
+			ftimage2_i_ModS2[i][j] = 0.0;
+			V_linterpAdj_r_ModS2[i][j] = 0.0;
+			V_linterpAdj_i_ModS2[i][j] = 0.0;
+			ftimage_r_ModS2[i][j] = 0.0;
+			ftimage_i_ModS2[i][j] = 0.0;
+			ftdata_r_ModS2[i][j] = 0.0;
+			ftdata_i_ModS2[i][j] = 0.0;
+			ftdata1_r_ModS2[i][j] = 0.0;
+			ftdata1_i_ModS2[i][j] = 0.0;
+			f_model_ModS2T[i][j] = 0.0;
+			ku_model_ModS2T[i][j] = 0.0;
+			fkz_model_ModS2T[i][j] = 0.0;
+			ftdata1_r_Model[i][j] = 0.0;
+			ftdata1_i_Model[i][j] = 0.0;
+			ftdata2_r_Model[i][j] = 0.0;
+			ftdata2_i_Model[i][j] = 0.0;
+			ftdata21_r_Model[i][j] = 0.0;
+			ftdata21_i_Model[i][j] = 0.0;
+			ftdata_r_Model[i][j] = 0.0;
+			ftdata_i_Model[i][j] = 0.0;
+			Vq1_linterp_r_Model[i][j] = 0.0;
+			Vq1_linterp_i_Model[i][j] = 0.0;
+			image1_r_Model[i][j] = 0.0;
+			image1_i_Model[i][j] = 0.0;
+			image2_r_Model[i][j] = 0.0;
+			image2_i_Model[i][j] = 0.0;
+		}
+		pG_r_linterpAdj_ModS2[i][0] = 0.0;
+		pG_i_linterpAdj_ModS2[i][0] = 0.0;
+		pF_r_linterpAdj_ModS2[i][0] = 0.0;
+		pF_i_linterpAdj_ModS2[i][0] = 0.0;
+	}
+
+	// paratmeters of CG
+
+	double** X_yaz = (double**)malloc((cols) * sizeof(double*));
+	for (int i = 0; i < ( cols); i++)
+	{
+		X_yaz[i] = (double*)malloc(cols * sizeof(double));
+		for (int j = 0; j < cols; j++)
+		{
+			X_yaz[i][j] = 0.0;
+		}
+	}
+	double** residual = (double**)malloc((cols) * sizeof(double*));
+	double** search_direction = (double**)malloc((cols) * sizeof(double*));
+	double** A_search_direction = (double**)malloc((cols) * sizeof(double*));
+	for (int i = 0; i < (cols); i++)
+	{
+		residual[i] = (double*)malloc(cols * sizeof(double));
+		search_direction[i] = (double*)malloc(cols * sizeof(double));
+		A_search_direction[i] = (double*)malloc(cols * sizeof(double));
+		for (int j = 0; j < cols; j++)
+		{
+			residual[i][j] = 0.0;
+			search_direction[i][j] = 0.0;
+			A_search_direction[i][j] = 0.0;
+		}
+	}
+
+	double errUTSR_a = 0;
+	int numIter, stagCount, maxIter;
+	numIter = 1; stagCount = 0; maxIter = 0;
+	// start timing 
+	srand(time(NULL));
+
+	printf("start While(1)\n");
+	while (1)
+	{
+		if (numIter > 1)
+		{
+			if (!isinf(beta))
+			{
+				while (1)
+				{
+					double n1fTemp = 0.0; double n1fTempAppr = 0.0; double n1Err = 0.0;
+					for (int i = 0; i < (M * cols); i++)
+					{
+						W[i][0] = 1 / (fabs(fTemp[i][0]) + beta);
+						n1fTemp = n1fTemp + fabs(fTemp[i][0]);
+						double s = (fabs(sqrt(W[i][0]) * fTemp[i][0]));
+						n1fTempAppr = n1fTempAppr + s * s;
+					}
+					n1Err = (n1fTemp - n1fTempAppr) / n1fTemp;
+					if (fabs(n1Err - cg_tol) > cg_tol / 10)
+					{
+						beta = beta / (n1Err / cg_tol);
+					}
+					else
+					{
+						break;
+					}
+				}
+			}
+		}
+		// Model1(x, W, dt, dx, ERMv, alpha, szData, tau0, Model, Filt, Rx)
+
+		//reshape(x,szData)
+		for (int i = 0; i < M; i++)
+		{
+			for (int j = 0; j < cols; j++)
+			{
+				res_x_szd[i][j] = X_cg[((j * cols) + i)][0];
+			}
+		}
+		//       save_matrix_as_bmp(res_x_szd, cols, M, "res_x_szd.bmp");
+		//    const char* filename6 = "res_x_szd.bmp";
+		//#ifdef _WIN32
+		//    system("start res_x_szd.bmp");
+		//#elif __APPLE__
+		//    system("open res_x_szd.bmp");
+		//#elif __linux__
+		//    system("xdg-open res_x_szd.bmp");
+		//#else
+		//    printf("Image sauvegardée sous %s\n", filename6);
+		//#endif
+
+				////ModS2(reshape(x, szData), dt, dx, ERMv, tau0, Mod, Rx)
+
+				//Data and image grids
+		if (numIter == 1)
+		{
+			double sign_f_ModS2;
+			for (int i = 0; i < nt_g; i++)
+			{
+				for (int j = 0; j < nu_g; j++)
+				{
+					f_ModS2[i][j] = (((double)(-nt_g / 2.0) + i) / dt) / nt_g;
+					ku_ModS2[i][j] = (((double)(-nu_g / 2.0) + j) / du) / nu_g;
+					sign_f_ModS2 = (f_ModS2[i][j] > 0) - (f_ModS2[i][j] < 0);
+					fkz_ModS2[i][j] = ERMv1 * sign_f_ModS2 * sqrt((ku_ModS2[i][j] * ku_ModS2[i][j]) + ((f_ModS2[i][j] / ERMv1) * (f_ModS2[i][j] / ERMv1)));
+				}
+			}
+		}
+		//        save_matrix_as_bmp(fkz_ModS2, nu_g, nt_g, "f_ModS2.bmp");
+		//        const char* filename7 = "f_ModS2.bmp";
+		//#ifdef _WIN32
+		//    system("start f_ModS2.bmp");
+		//#elif __APPLE__
+		//    system("open f_ModS2.bmp");
+		//#elif __linux__
+		//    system("xdg-open f_ModS2.bmp");
+		//#else
+		//    printf("Image sauvegardée sous %s\n", filename7);
+		//#endif
+
+				// fft2(res_x_szd, nt, nu)
+		double sum_ftimage1_r_ModS2 = 0.0;
+		double sum_ftimage1_i_ModS2 = 0.0;
+		for (int k1 = 0; k1 < nt_g; k1++)
+		{
+			for (int k2 = 0; k2 < nu_g; k2++)
+			{
+				for (int n1 = 0; n1 < M; n1++)
+				{
+					for (int n2 = 0; n2 < cols; n2++)
+					{
+						double angle = 2 * pi * ((double)(k1 * n1) / nt_g + (double)(k2 * n2) / nu_g);
+						sum_ftimage1_r_ModS2 = sum_ftimage1_r_ModS2 + res_x_szd[n1][n2] * cos(angle);
+						sum_ftimage1_i_ModS2 = sum_ftimage1_i_ModS2 - res_x_szd[n1][n2] * sin(angle);
+					}
+				}
+				ftimage1_r_ModS2[k1][k2] = sum_ftimage1_r_ModS2;
+				ftimage1_i_ModS2[k1][k2] = sum_ftimage1_i_ModS2;
+				sum_ftimage1_i_ModS2 = 0.0;
+				sum_ftimage1_r_ModS2 = 0.0;
+			}
+		}//fin FFT2
+
+		//fftshift
+		for (int i = 0; i < nt_g; i++)
+		{
+			for (int j = 0; j < nu_g; j++)
+			{
+				if (b_fftshift == 1)
+				{
+					if (j <= (int)(nu_g / 2))
+					{
+						ftimage21_r_ModS2[i][j] = ftimage1_r_ModS2[i][j + (int)(nu_g / 2) + 1];
+						ftimage21_i_ModS2[i][j] = ftimage1_i_ModS2[i][j + (int)(nu_g / 2) + 1];
+					}
+					else
+					{
+						ftimage21_r_ModS2[i][j] = ftimage1_r_ModS2[i][j - (int)(nu_g / 2)];
+						ftimage21_i_ModS2[i][j] = ftimage1_i_ModS2[i][j - (int)(nu_g / 2)];
+					}
+				}
+				if (b_fftshift == 0)
+				{
+					if (j < (int)(nu_g / 2))
+					{
+						ftimage21_r_ModS2[i][j] = ftimage1_r_ModS2[i][j + (int)(nu_g / 2)];
+						ftimage21_i_ModS2[i][j] = ftimage1_i_ModS2[i][j + (int)(nu_g / 2)];
+					}
+					else
+					{
+						ftimage21_r_ModS2[i][j] = ftimage1_r_ModS2[i][j - (int)(nu_g / 2)];
+						ftimage21_i_ModS2[i][j] = ftimage1_i_ModS2[i][j - (int)(nu_g / 2)];
+					}
+				}
+			}
+		}
+		for (int i = 0; i < nt_g; i++)
+		{
+
+			for (int j = 0; j < nu_g; j++)
+			{
+				if (a_fftshift == 1)
+				{
+					if (i <= (nt_g / 2))
+					{
+
+						ftimage2_r_ModS2[i][j] = ftimage21_r_ModS2[i + (int)(nt_g / 2) + 1][j];
+						ftimage2_i_ModS2[i][j] = ftimage21_i_ModS2[i + (int)(nt_g / 2) + 1][j];
+					}
+					else
+					{
+						ftimage2_r_ModS2[i][j] = ftimage21_r_ModS2[i - (int)(nt_g / 2)][j];
+						ftimage2_i_ModS2[i][j] = ftimage21_i_ModS2[i - (int)(nt_g / 2)][j];
+					}
+				}
+				if (a_fftshift == 0)
+				{
+					if (i < (nt_g / 2))
+					{
+						ftimage2_r_ModS2[i][j] = ftimage21_r_ModS2[i + (int)(nt_g / 2)][j];
+						ftimage2_i_ModS2[i][j] = ftimage21_i_ModS2[i + (int)(nt_g / 2)][j];
+					}
+					else
+					{
+						ftimage2_r_ModS2[i][j] = ftimage21_r_ModS2[i - (int)(nt_g / 2)][j];
+						ftimage2_i_ModS2[i][j] = ftimage21_i_ModS2[i - (int)(nt_g / 2)][j];
+					}
+				}
+			}
+		}//fin fftshift
+
+//		save_matrix_as_bmp(ftimage2_r_ModS2, nu_g, nt_g, "ftimage1_r_ModS2.bmp");
+//		const char* filename8 = "ftimage1_r_ModS2.bmp";
+//#ifdef _WIN32
+//		system("start ftimage1_r_ModS2.bmp");
+//#elif __APPLE__
+//		system("open ftimage1_r_ModS2.bmp");
+//#elif __linux__
+//		system("xdg-open ftimage1_r_ModS2.bmp");
+//#else
+//		printf("Image sauvegardée sous %s\n", filename8);
+//#endif
+
+		//linterpAdj(f(:,1), fkz, ftimage);
+		for (int i = 0; i < nt_g; i++)
+		{
+			for (int j = 0; j < nu_g; j++)
+			{
+				V_linterpAdj_r_ModS2[i][j] = 0.0;
+				V_linterpAdj_i_ModS2[i][j] = 0.0;
+				pG_r_linterpAdj_ModS2[i][0] = 0.0;
+				pG_i_linterpAdj_ModS2[i][0] = 0.0;
+				pF_r_linterpAdj_ModS2[i][0] = 0.0;
+				pF_i_linterpAdj_ModS2[i][0] = 0.0;
+			}
+		}
+		double dx_linterpAdj_ModS2 = f_ModS2[1][0] - f_ModS2[0][0];
+		for (int i = 0; i < nu_g; i++)
+		{
+			for (int j = 0; j < nt_g; j++)
+			{
+				double f1_linterpAdj_ModS2 = (fkz_ModS2[j][i] - f_ModS2[0][0]) / dx_linterpAdj_ModS2;
+				int fMask_1 = !((fkz_ModS2[j][i] < f_ModS2[0][0]) | (fkz_ModS2[j][i] > f_ModS2[(nt_g - 1)][0]));
+				double f_linterpAdj_ModS2 = f1_linterpAdj_ModS2 * fMask_1;
+				int im_linterpAdj_ModS2 = (int)floor(f_linterpAdj_ModS2);
+				int im2Inval_linterpAdj_ModS2 = (im_linterpAdj_ModS2 + 2 > nt_g) ? 1 : 0;
+				double fx_linterpAdj_ModS2 = f_linterpAdj_ModS2 - (double)im_linterpAdj_ModS2;
+				double gx_linterpAdj_ModS2 = 1.0 - fx_linterpAdj_ModS2;
+				if (fMask_1 == 1)
+				{
+					pG_r_linterpAdj_ModS2[im_linterpAdj_ModS2][0] = pG_r_linterpAdj_ModS2[im_linterpAdj_ModS2][0] + gx_linterpAdj_ModS2 * ftimage2_r_ModS2[j][i];
+					pG_i_linterpAdj_ModS2[im_linterpAdj_ModS2][0] = pG_i_linterpAdj_ModS2[im_linterpAdj_ModS2][0] + gx_linterpAdj_ModS2 * ftimage2_i_ModS2[j][i];
+					if (im2Inval_linterpAdj_ModS2 > 0)
+					{
+						pF_r_linterpAdj_ModS2[nt_g - 1][0] = 0.0;
+						pF_i_linterpAdj_ModS2[nt_g - 1][0] = 0.0;
+					}
+					else
+					{
+						pF_r_linterpAdj_ModS2[im_linterpAdj_ModS2 + 1][0] = pF_r_linterpAdj_ModS2[im_linterpAdj_ModS2 + 1][0] + fx_linterpAdj_ModS2 * ftimage2_r_ModS2[j][i];
+						pF_i_linterpAdj_ModS2[im_linterpAdj_ModS2 + 1][0] = pF_i_linterpAdj_ModS2[im_linterpAdj_ModS2 + 1][0] + fx_linterpAdj_ModS2 * ftimage2_i_ModS2[j][i];
+					}
+				}
+			}
+			for (int j = 0; j < nt_g; j++)
+			{
+				V_linterpAdj_r_ModS2[j][i] = pG_r_linterpAdj_ModS2[j][0] + pF_r_linterpAdj_ModS2[j][0];
+				V_linterpAdj_i_ModS2[j][i] = pG_i_linterpAdj_ModS2[j][0] + pF_i_linterpAdj_ModS2[j][0];
+				pG_r_linterpAdj_ModS2[j][0] = 0.0;
+				pG_i_linterpAdj_ModS2[j][0] = 0.0;
+				pF_r_linterpAdj_ModS2[j][0] = 0.0;
+				pF_i_linterpAdj_ModS2[j][0] = 0.0;
+			}
+		}// fin linterpAdj
+//		save_matrix_as_bmp(V_linterpAdj_r_ModS2, nu_g, nt_g, "V_linterpAdj_r_ModS2.bmp");
+//		const char* filename9 = "V_linterpAdj_r_ModS2.bmp";
+//#ifdef _WIN32
+//		system("start V_linterpAdj_r_ModS2.bmp");
+//#elif __APPLE__
+//		system("open V_linterpAdj_r_ModS2.bmp");
+//#elif __linux__
+//		system("xdg-open V_linterpAdj_r_ModS2.bmp");
+//#else
+//		printf("Image sauvegardée sous %s\n", filename9);
+//#endif
+		// tau0
+		for (int i = 0; i < nt_g; i++)
+		{
+			for (int j = 0; j < nu_g; j++)
+			{
+				double angle = 2 * pi * (double)(fkz_ModS2[i][j] - f_ModS2[i][j]) * tau0;
+				double angcos = cos(angle);
+				double angsin = sin(angle);
+				double re = V_linterpAdj_r_ModS2[i][j] * angcos - V_linterpAdj_i_ModS2[i][j] * angsin;
+				double im = V_linterpAdj_i_ModS2[i][j] * angcos + V_linterpAdj_r_ModS2[i][j] * angsin;
+				ftimage_r_ModS2[i][j] = re * Model_r[i][j] - im * Model_i[i][j];
+				ftimage_i_ModS2[i][j] = im * Model_r[i][j] + re * Model_i[i][j];
+			}
+		}
+
+		//		save_matrix_as_bmp(ftimage_r_ModS2, nu_g, nt_g, "ftimage_r_ModS2.bmp");
+		//		const char* filename10 = "ftimage_r_ModS2.bmp";
+		//#ifdef _WIN32
+		//		system("start ftimage_r_ModS2.bmp");
+		//#elif __APPLE__
+		//		system("open ftimage_r_ModS2.bmp");
+		//#elif __linux__
+		//		system("xdg-open ftimage_r_ModS2.bmp");
+		//#else
+		//		printf("Image sauvegardée sous %s\n", filename10);
+		//#endif
+
+				//ifftshift(ftdata)
+		for (int i = 0; i < nt_g; i++)
+		{
+			for (int j = 0; j < nu_g; j++)
+			{
+				if (b_fftshift == 1)
+				{
+					if (j <= (int)(nu_g / 2))
+					{
+						ftdata_r_ModS2[i][j] = ftimage_r_ModS2[i][j + (int)(nu_g / 2)];
+						ftdata_i_ModS2[i][j] = ftimage_i_ModS2[i][j + (int)(nu_g / 2)];
+					}
+					else
+					{
+						ftdata_r_ModS2[i][j] = ftimage_r_ModS2[i][j - ((int)(nu_g / 2) + 1)];
+						ftdata_i_ModS2[i][j] = ftimage_i_ModS2[i][j - ((int)(nu_g / 2) + 1)];
+					}
+				}
+				if (b_fftshift == 0)
+				{
+					if (j < (int)(nu_g / 2))
+					{
+						ftdata_r_ModS2[i][j] = ftimage_r_ModS2[i][j + (int)(nu_g / 2)];
+						ftdata_i_ModS2[i][j] = ftimage_i_ModS2[i][j + (int)(nu_g / 2)];
+					}
+					else
+					{
+						ftdata_r_ModS2[i][j] = ftimage_r_ModS2[i][j - (int)(nu_g / 2)];
+						ftdata_i_ModS2[i][j] = ftimage_i_ModS2[i][j - (int)(nu_g / 2)];
+					}
+				}
+			}
+		}
+		for (int i = 0; i < nt_g; i++)
+		{
+			for (int j = 0; j < nu_g; j++)
+			{
+				if (a_fftshift == 1)
+				{
+					if (i <= (nt_g / 2))
+					{
+
+						ftdata1_r_ModS2[i][j] = ftdata_r_ModS2[i + (int)(nt_g / 2)][j];
+						ftdata1_i_ModS2[i][j] = ftdata_i_ModS2[i + (int)(nt_g / 2)][j];
+					}
+					else
+					{
+						ftdata1_r_ModS2[i][j] = ftdata_r_ModS2[i - ((int)(nt_g / 2) + 1)][j];
+						ftdata1_i_ModS2[i][j] = ftdata_i_ModS2[i - ((int)(nt_g / 2) + 1)][j];
+					}
+				}
+				if (a_fftshift == 0)
+				{
+					if (i < (nt_g / 2))
+					{
+						ftdata1_r_ModS2[i][j] = ftdata_r_ModS2[i + (int)(nt_g / 2)][j];
+						ftdata1_i_ModS2[i][j] = ftdata_i_ModS2[i + (int)(nt_g / 2)][j];
+					}
+					else
+					{
+						ftdata1_r_ModS2[i][j] = ftdata_r_ModS2[i - (int)(nt_g / 2)][j];
+						ftdata1_i_ModS2[i][j] = ftdata_i_ModS2[i - (int)(nt_g / 2)][j];
+					}
+				}
+				//printf("%e\t", ftdata1_r_ModS2[i][j]);
+				//printf("=%e\n", vq1_i_ModS2T[i][j]);
+			}
+			//printf("\n");
+		}
+
+		//		save_matrix_as_bmp(ftdata1_r_ModS2, nu_g, nt_g, "ftdata1_r_ModS2.bmp");
+		//		const char* filename11 = "ftdata1_r_ModS2.bmp";
+		//#ifdef _WIN32
+		//		system("start ftdata1_r_ModS2.bmp");
+		//#elif __APPLE__
+		//		system("open ftdata1_r_ModS2.bmp");
+		//#elif __linux__
+		//		system("xdg-open ftdata1_r_ModS2.bmp");
+		//#else
+		//		printf("Image sauvegardée sous %s\n", filename11);
+		//#endif
+
+				//ifft2
+		cts_ifft = (nt_g * nu_g);
+		for (int n1 = 0; n1 < M; n1++)
+		{
+			for (int n2 = 0; n2 < cols; n2++)
+			{
+				double som_r = 0.0;
+				for (int k1 = 0; k1 < nt_g; k1++)
+				{
+					for (int k2 = 0; k2 < nu_g; k2++)
+					{
+						double angle = 2.0 * pi * ((double)(k1 * n1) / nt_g + (double)(k2 * n2) / nu_g);
+						double cosangle = cos(angle);
+						double sinangle = sin(angle);
+						som_r = som_r + ftdata1_r_ModS2[k1][k2] * cosangle - ftdata1_i_ModS2[k1][k2] * sinangle;
+					}
+				}
+				g[n1][n2] = (som_r / cts_ifft) * Rx;
+			}
+		}// fin ifft
+//		save_matrix_as_bmp(g, cols, M, "g.bmp");
+//		const char* filename12 = "g.bmp";
+//#ifdef _WIN32
+//		system("start g.bmp");
+//#elif __APPLE__
+//		system("open g.bmp");
+//#elif __linux__
+//		system("xdg-open g.bmp");
+//#else
+//		printf("Image sauvegardée sous %s\n", filename12);
+//#endif
+
+		//Applies adjoint operator
+		//y = ModS2T(g , dt, dx, ERMv, tau0, Filt, Rx);
+		//meshgrid(ku,f)
+		if (numIter == 1)
+		{
+			double sign_f;
+			for (int i = 0; i < nt_g; i++)
+			{
+				for (int j = 0; j < nu_g; j++)
+				{
+					f_model_ModS2T[i][j] = (((double)(-nt_g / 2.0) + i) / dt) / nt_g;
+					ku_model_ModS2T[i][j] = (((double)(-nu_g / 2.0) + j) / du) / nu_g;
+					sign_f = (f_model_ModS2T[i][j] > 0) - (f_model_ModS2T[i][j] < 0);
+					fkz_model_ModS2T[i][j] = ERMv1 * sign_f * sqrt((ku_model_ModS2T[i][j] * ku_model_ModS2T[i][j]) + ((f_model_ModS2T[i][j] / ERMv1) * (f_model_ModS2T[i][j] / ERMv1)));
+				}
+			}
+		}
+
+		//		save_matrix_as_bmp(fkz_model_ModS2T, nu_g, nt_g, "f_model_ModS2T.bmp");
+		//		const char* filename13 = "f_model_ModS2T.bmp";
+		//#ifdef _WIN32
+		//		system("start f_model_ModS2T.bmp");
+		//#elif __APPLE__
+		//		system("open f_model_ModS2T.bmp");
+		//#elif __linux__
+		//		system("xdg-open f_model_ModS2T.bmp");
+		//#else
+		//		printf("Image sauvegardée sous %s\n", filename13);
+		//#endif
+
+				//Converting data to frquency domain
+				//// FFT2(g, nt_g, nu_g)
+		double sum_ftdata1_r_Model = 0.0;
+		double sum_ftdata1_i_Model = 0.0;
+		for (int k1 = 0; k1 < nt_g; k1++)
+		{
+			for (int k2 = 0; k2 < nu_g; k2++)
+			{
+				for (int n1 = 0; n1 < M; n1++)
+				{
+					for (int n2 = 0; n2 < cols; n2++)
+					{
+						double angle = 2 * pi * ((double)(k1 * n1) / nt_g + (double)(k2 * n2) / nu_g);
+						sum_ftdata1_r_Model = sum_ftdata1_r_Model + g[n1][n2] * cos(angle);
+						sum_ftdata1_i_Model = sum_ftdata1_i_Model - g[n1][n2] * sin(angle);
+					}
+				}
+				ftdata1_r_Model[k1][k2] = sum_ftdata1_r_Model;
+				ftdata1_i_Model[k1][k2] = sum_ftdata1_i_Model;
+				sum_ftdata1_r_Model = 0.0;
+				sum_ftdata1_i_Model = 0.0;
+			}
+		}
+		//		save_matrix_as_bmp(ftdata1_r_Model, nu_g, nt_g, "ftdata1_r_Model.bmp");
+		//		const char* filename14 = "ftdata1_r_Model.bmp";
+		//#ifdef _WIN32
+		//		system("start ftdata1_r_Model.bmp");
+		//#elif __APPLE__
+		//		system("open ftdata1_r_Model.bmp");
+		//#elif __linux__
+		//		system("xdg-open ftdata1_r_Model.bmp");
+		//#else
+		//		printf("Image sauvegardée sous %s\n", filename14);
+		//#endif
+
+				////fftshift
+		for (int i = 0; i < nt_g; i++)
+		{
+			for (int j = 0; j < nu_g; j++)
+			{
+
+				if (b_fftshift == 1)
+				{
+					if (j <= (int)(nu_g / 2))
+					{
+						ftdata2_r_Model[i][j] = ftdata1_r_Model[i][j + (int)(nu_g / 2) + 1];
+						ftdata2_i_Model[i][j] = ftdata1_i_Model[i][j + (int)(nu_g / 2) + 1];
+					}
+					else
+					{
+						ftdata2_r_Model[i][j] = ftdata1_r_Model[i][j - (int)(nu_g / 2)];
+						ftdata2_i_Model[i][j] = ftdata1_i_Model[i][j - (int)(nu_g / 2)];
+					}
+				}
+				if (b_fftshift == 0)
+				{
+					if (j < (int)(nu_g / 2))
+					{
+						ftdata2_r_Model[i][j] = ftdata1_r_Model[i][j + (int)(nu_g / 2)];
+						ftdata2_i_Model[i][j] = ftdata1_i_Model[i][j + (int)(nu_g / 2)];
+					}
+					else
+					{
+						ftdata2_r_Model[i][j] = ftdata1_r_Model[i][j - (int)(nu_g / 2)];
+						ftdata2_i_Model[i][j] = ftdata1_i_Model[i][j - (int)(nu_g / 2)];
+					}
+				}
+			}
+		}
+		for (int i = 0; i < nt_g; i++)
+		{
+			for (int j = 0; j < nu_g; j++)
+			{
+				if (a_fftshift == 1)
+				{
+					if (i <= (nt_g / 2))
+					{
+
+						ftdata21_r_Model[i][j] = ftdata2_r_Model[i + (int)(nt_g / 2) + 1][j];
+						ftdata21_i_Model[i][j] = ftdata2_i_Model[i + (int)(nt_g / 2) + 1][j];
+					}
+					else
+					{
+						ftdata21_r_Model[i][j] = ftdata2_r_Model[i - (int)(nt_g / 2)][j];
+						ftdata21_i_Model[i][j] = ftdata2_i_Model[i - (int)(nt_g / 2)][j];
+					}
+				}
+				if (a_fftshift == 0)
+				{
+					if (i < (nt_g / 2))
+					{
+						ftdata21_r_Model[i][j] = ftdata2_r_Model[i + (int)(nt_g / 2)][j];
+						ftdata21_i_Model[i][j] = ftdata2_i_Model[i + (int)(nt_g / 2)][j];
+					}
+					else
+					{
+						ftdata21_r_Model[i][j] = ftdata2_r_Model[i - (int)(nt_g / 2)][j];
+						ftdata21_i_Model[i][j] = ftdata2_i_Model[i - (int)(nt_g / 2)][j];
+					}
+				}
+			}
+		}
+		// fin fftshift  
+
+//		save_matrix_as_bmp(ftdata21_r_Model, nu_g, nt_g, "ftdata21_r_Model.bmp");
+//		const char* filename15 = "ftdata21_r_Model.bmp";
+//#ifdef _WIN32
+//		system("start ftdata21_r_Model.bmp");
+//#elif __APPLE__
+//		system("open ftdata21_r_Model.bmp");
+//#elif __linux__
+//		system("xdg-open ftdata21_r_Model.bmp");
+//#else
+//		printf("Image sauvegardée sous %s\n", filename15);
+//#endif
+
+		//// tau0
+		for (int i = 0; i < nt_g; i++)
+		{
+
+			for (int j = 0; j < nu_g; j++)
+			{
+				double angle = 2 * pi * (double)(fkz_model_ModS2T[i][j] - f_model_ModS2T[i][j]) * tau0;
+				double angcos = cos(angle);
+				double angsin = -sin(angle);
+				double re = ftdata21_r_Model[i][j] * angcos - ftdata21_i_Model[i][j] * angsin;
+				double im = ftdata21_i_Model[i][j] * angcos + ftdata21_r_Model[i][j] * angsin;
+				ftdata_r_Model[i][j] = re * Filt_r[i][j] - im * Filt_i[i][j];
+				ftdata_i_Model[i][j] = re * Filt_i[i][j] + im * Filt_r[i][j];
+			}
+
+		}
+
+		//		save_matrix_as_bmp(ftdata_r_Model, nu_g, nt_g, "ftdata_r_Model.bmp");
+		//		const char* filename16 = "ftdata_r_Model.bmp";
+		//#ifdef _WIN32
+		//		system("start ftdata_r_Model.bmp");
+		//#elif __APPLE__
+		//		system("open ftdata_r_Model.bmp");
+		//#elif __linux__
+		//		system("xdg-open ftdata_r_Model.bmp");
+		//#else
+		//		printf("Image sauvegardée sous %s\n", filename16);
+		//#endif
+
+				////Generating image spectrum (by linear interpolation)
+				//// linterp(f(:,1), ftdata, fkz);
+		for (int i = 0; i < nt_g; i++)
+		{
+			for (int j = 0; j < nu_g; j++)
+			{
+				Vq1_linterp_r_Model[i][j] = 0.0;
+				Vq1_linterp_i_Model[i][j] = 0.0;
+			}
+		}
+		double dx_linterp_Model = f_model_ModS2T[1][0] - f_model_ModS2T[0][0];
+
+		for (int i = 0; i < nu_g; i++)
+		{
+			for (int j = 0; j < nt_g; j++)
+			{
+				double f1_model = (fkz_model_ModS2T[j][i] - f_model_ModS2T[0][0]) / dx_linterp_Model;
+				int fMask_model = !((fkz_model_ModS2T[j][i] < f_model_ModS2T[0][0]) | (fkz_model_ModS2T[j][i] > f_model_ModS2T[(nt_g - 1)][0]));
+				double f_model = f1_model * fMask_model;
+				int im_model = (int)floor(f_model);
+				int im2Inval_model = (im_model + 2 > nt_g - 1) ? 1 : 0;
+
+				double fx = f_model - (double)im_model;
+				double gx = 1.0 - fx;
+				if (fMask_model == 1)
+				{
+					if (im2Inval_model > 0)
+					{
+						Vq1_linterp_r_Model[j][i] = gx * ftdata_r_Model[im_model][i];
+						Vq1_linterp_i_Model[j][i] = gx * ftdata_i_Model[im_model][i];
+
+					}
+					else
+					{
+						Vq1_linterp_r_Model[j][i] = gx * ftdata_r_Model[im_model][i] + fx * ftdata_r_Model[im_model + 1][i];
+						Vq1_linterp_i_Model[j][i] = gx * ftdata_i_Model[im_model][i] + fx * ftdata_i_Model[im_model + 1][i];
+					}
+				}
+
+			}
+		}// fin linterp
+
+//		save_matrix_as_bmp(Vq1_linterp_r_Model, nu_g, nt_g, "Vq1_linterp_r_Model.bmp");
+//		const char* filename17 = "Vq1_linterp_r_Model.bmp";
+//#ifdef _WIN32
+//		system("start Vq1_linterp_r_Model.bmp");
+//#elif __APPLE__
+//		system("open Vq1_linterp_r_Model.bmp");
+//#elif __linux__
+//		system("xdg-open Vq1_linterp_r_Model.bmp");
+//#else
+//		printf("Image sauvegardée sous %s\n", filename17);
+//#endif
+
+		// Converting image to space domain
+		//ifftshift(Vq1_linterp_r_Model)
+		for (int i = 0; i < nt_g; i++)
+		{
+			for (int j = 0; j < nu_g; j++)
+			{
+				if (b_fftshift == 1)
+				{
+					if (j <= (int)(nu_g / 2))
+					{
+						image1_r_Model[i][j] = Vq1_linterp_r_Model[i][j + (int)(nu_g / 2)];
+						image1_i_Model[i][j] = Vq1_linterp_i_Model[i][j + (int)(nu_g / 2)];
+					}
+					else
+					{
+						image1_r_Model[i][j] = Vq1_linterp_r_Model[i][j - ((int)(nu_g / 2) + 1)];
+						image1_i_Model[i][j] = Vq1_linterp_i_Model[i][j - ((int)(nu_g / 2) + 1)];
+					}
+				}
+				if (b_fftshift == 0)
+				{
+					if (j < (int)(nu_g / 2))
+					{
+						image1_r_Model[i][j] = Vq1_linterp_r_Model[i][j + (int)(nu_g / 2)];
+						image1_i_Model[i][j] = Vq1_linterp_i_Model[i][j + (int)(nu_g / 2)];
+					}
+					else
+					{
+						image1_r_Model[i][j] = Vq1_linterp_r_Model[i][j - (int)(nu_g / 2)];
+						image1_i_Model[i][j] = Vq1_linterp_i_Model[i][j - (int)(nu_g / 2)];
+					}
+				}
+			}
+		}
+		for (int i = 0; i < nt_g; i++)
+		{
+			for (int j = 0; j < nu_g; j++)
+			{
+				if (a_fftshift == 1)
+				{
+					if (i <= (nt_g / 2))
+					{
+
+						image2_r_Model[i][j] = image1_r_Model[i + (int)(nt_g / 2)][j];
+						image2_i_Model[i][j] = image1_i_Model[i + (int)(nt_g / 2)][j];
+					}
+					else
+					{
+						image2_r_Model[i][j] = image1_r_Model[i - ((int)(nt_g / 2) + 1)][j];
+						image2_i_Model[i][j] = image1_i_Model[i - ((int)(nt_g / 2) + 1)][j];
+					}
+				}
+				if (a_fftshift == 0)
+				{
+					if (i < (nt_g / 2))
+					{
+						image2_r_Model[i][j] = image1_r_Model[i + (int)(nt_g / 2)][j];
+						image2_i_Model[i][j] = image1_i_Model[i + (int)(nt_g / 2)][j];
+					}
+					else
+					{
+						image2_r_Model[i][j] = image1_r_Model[i - (int)(nt_g / 2)][j];
+						image2_i_Model[i][j] = image1_i_Model[i - (int)(nt_g / 2)][j];
+					}
+				}
+			}
+		}
+		// fin ifftshift
+
+//		save_matrix_as_bmp(image2_r_Model, nu_g, nt_g, "image2_r_Model.bmp");
+//		const char* filename18 = "image2_r_Model.bmp";
+//#ifdef _WIN32
+//		system("start image2_r_Model.bmp");
+//#elif __APPLE__
+//		system("open image2_r_Model.bmp");
+//#elif __linux__
+//		system("xdg-open image2_r_Model.bmp");
+//#else
+//		printf("Image sauvegardée sous %s\n", filename18);
+//#endif
+
+		// ifft
+		cts_ifft = (nt_g * nu_g);
+		for (int n1 = 0; n1 < M; n1++)
+		{
+			for (int n2 = 0; n2 < cols; n2++)
+			{
+				double som_r = 0.0;
+				for (int k1 = 0; k1 < nt_g; k1++)
+				{
+					for (int k2 = 0; k2 < nu_g; k2++)
+					{
+						double angle = 2.0 * pi * ((double)(k1 * n1) / nt_g + (double)(k2 * n2) / nu_g);
+						double cosangle = cos(angle);
+						double sinangle = sin(angle);
+						som_r = som_r + image2_r_Model[k1][k2] * cosangle - image2_i_Model[k1][k2] * sinangle;
+					}
+				}
+				Y1_Model[n1][n2] = (som_r / cts_ifft) * Rx;
+			}
+		}// fin ifft
+
+//		save_matrix_as_bmp(Y1_Model, cols, M, "Y1_Model.bmp");
+//		const char* filename19 = "Y1_Model.bmp";
+//#ifdef _WIN32
+//		system("start Y1_Model.bmp");
+//#elif __APPLE__
+//		system("open Y1_Model.bmp");
+//#elif __linux__
+//		system("xdg-open Y1_Model.bmp");
+//#else
+//		printf("Image sauvegardée sous %s\n", filename19);
+//#endif
+
+		for (int i = 0; i < M; i++)
+		{
+			for (int j = 0; j < cols; j++)
+			{
+				Y_Model[(i * cols) + j][0] = Y1_Model[i][j] + alpha * alpha * W[(i * cols) + j][0] * X_cg[(i * cols) + j][0];
+				Y1_Model[i][j]=Y1_Model[i][j] + alpha * alpha * W[(i * cols) + j][0] * X_cg[(i * cols) + j][0];
+			}
+		}
+
+		// CG 
+		int k = 0;
+		for (int i = 0; i < cols; i++)
+		{
+			double sumx, old_resid_norm = 0, sum2;
+			for (int i1 = 0; i1 < cols; i1++)
+			{
+				sumx = 0;
+				for (int j = 0; j < cols; j++)
+				{
+					sumx += Y1_Model[i1][j] *X_yaz[j][i];
+				}
+				residual[i1][i] = HTg_1[i1][i] - sumx;
+				search_direction[i1][i] = residual[i1][i];
+				old_resid_norm += residual[i1][i] * residual[i1][i];
+			}
+			old_resid_norm = sqrt(old_resid_norm);
+			
+			while (old_resid_norm > 0.0001)
+			{
+				sum2 = 0;
+				for (int i1 = 0; i1 < cols; i1++)
+				{
+					sumx = 0;
+					for (int j = 0; j < cols; j++)
+					{
+						sumx += Y1_Model[i1][j] * search_direction[j][i];
+					}
+					A_search_direction[i1][i] = sumx;
+					sum2 += A_search_direction[i1][i] * search_direction[i1][i];
+				}
+				double step_size = old_resid_norm * old_resid_norm / sum2;
+				if (step_size < 0)break;
+				sumx = 0;
+				for (int i1 = 0; i1 < cols; i1++)
+				{
+					X_yaz[i1][i] += step_size * search_direction[i1][i];
+					residual[i1][i] = residual[i1][i] - step_size * A_search_direction[i1][i];
+					sumx += residual[i1][i] * residual[i1][i];
+				}
+				double new_resid_norm = sqrt(sumx);
+				for (int i1 = 0; i1 < cols; i1++)
+				{
+					search_direction[i1][i] = residual[i1][i] + ((new_resid_norm / old_resid_norm) * (new_resid_norm / old_resid_norm)) * search_direction[i1][i];
+				}
+				//printf("%e ", X_yaz[0][i]);
+				old_resid_norm = new_resid_norm;
+				k = k + 1;
+				
+
+			}
+			printf("%d \n", i);
+		}
+		printf("k=%d\n", k);
+
+
+		for (int i = 0; i < cols; i++)
+		{
+			for (int j = 0; j < cols; j++)
+			{
+				//X_cg[i*cols+j][0] = X_yaz[i][j];
+				if (X_cg[i * cols + j][0] < 0)
+				{
+					X_cg[i * cols + j][0] = 0.0;
+				}
+			}
+			
+		}
+		break;
+
+	}
+	//Reshape found solution as a matrix
+	// outputRaw = reshape(f, szData);
+	double** outputRaw = (double**)malloc(M * sizeof(double*));
+	for (int i = 0; i < M; i++)
+	{
+		outputRaw[i] = (double*)malloc(cols * sizeof(double));
+		for (int j = 0; j < cols; j++)
+		{
+			outputRaw[i][j] = X_cg[i * cols + j][0];
+			//printf("%e ", X_yaz[i][j]);
+		}
+		//printf("\n");
+	}
+	free(Vq1_linterp_r_Model); free(Vq1_linterp_i_Model);
+	free(HTg); free(fTemp); free(W); free(g); free(Y1_Model);
+	free(Y_Model); free(ku_ModS2); free(res_x_szd);
+	free(ftimage1_r_ModS2); free(ftimage1_i_ModS2);
+	free(ftimage21_r_ModS2); free(ftimage21_i_ModS2);
+	free(ftimage2_r_ModS2); free(ftimage2_i_ModS2);
+	free(pG_r_linterpAdj_ModS2); free(pG_i_linterpAdj_ModS2);
+	free(pF_r_linterpAdj_ModS2); free(pF_i_linterpAdj_ModS2);
+	free(V_linterpAdj_r_ModS2); free(V_linterpAdj_i_ModS2);
+	free(ftimage_r_ModS2); free(ftimage_i_ModS2);
+	free(fkz_ModS2); free(f_ModS2);
+	free(ftdata_r_ModS2); free(ftdata_i_ModS2);
+	free(ftdata1_r_ModS2); free(ftdata1_i_ModS2);
+	free(ku_model_ModS2T); free(ftdata1_i_Model); free(ftdata1_r_Model);
+	free(ftdata2_r_Model); free(ftdata2_i_Model);
+	free(ftdata21_r_Model); free(ftdata21_i_Model);
+	free(ftdata_r_Model); free(ftdata_i_Model);
+	free(f_model_ModS2T); free(fkz_model_ModS2T);
+	free(image1_r_Model); free(image1_i_Model);
+	free(image2_r_Model); free(image2_i_Model);
+	tEnd = clock();
+	time_elapsed = ((double)(tEnd - tAlg)) / CLOCKS_PER_SEC;
+		printf("Elapsed time is : %f seconds.\n", time_elapsed);
+		save_matrix_as_bmp(outputRaw, cols, M, "output.bmp");
+		const char* filename = "output.bmp";
+	#ifdef _WIN32
+		system("start output.bmp");
+	#elif __APPLE__
+		system("open output.bmp");
+	#elif __linux__
+		system("xdg-open output.bmp");
+	#else
+		printf("Image sauvegardée sous %s\n", filename);
+	#endif
+		free(outputRaw);
+	free(Model_r); free(Model_i);
+	free(Filt_r); free(Filt_i);
+	free(AscanValues_ptAco40dB); free(timeScale_ptAco40dB);
+	free(S_t_u);
+
+}
+
+
+
+int nextpow2(int n) {
+	int exp = 0;
+	if (n < 1) return 0;
+	n--;
+	while (n > 0) {
+		n >>= 1;
+		exp++;
+	}
+	return exp;
+}
+
+double sinc(double x) {
+	if (x == 0) {
+		return 1.0;
+	}
+	else {
+		return sin(pi * x) / (pi * x);
+	}
+}
+
+//double** X_pcg = (double**)malloc((M * cols) * sizeof(double*));
+//double** xmin_pcg = (double**)malloc((M * cols) * sizeof(double*));
+//double** r_pcg = (double**)malloc((M * cols) * sizeof(double*));
+//double** y_pcg = (double**)malloc((M * cols) * sizeof(double*));
+//double** z_pcg = (double**)malloc((M * cols) * sizeof(double*));
+//double** p_pcg = (double**)malloc((M * cols) * sizeof(double*));
+//double** q_pcg = (double**)malloc((M * cols) * sizeof(double*));
+
+////
+////
+//// PCG
+////int flag_pcg, iter_pcg;
+////int while_2 = 0;
+////while (while_2 == 0)
+////{
+////	printf("pcg\n");
+////	while_2 += 1;
+////	 Preconditioned Conjugate Gradient method 
+////	 [f, flag, ~, iter] = pcg(yazHTg(:), cg_tol, M*N, [], [], fTemp);
+////	 iterchk(A);
+////	 afun = Y_Model;
+////	int m_pcg = M * cols, n_pcg = 1;
+////	Assign default values to unspecified parameters
+////	int warned_pcg = 0, maxit_pcg;
+////	maxit_pcg = M * cols;
+////	if (maxit_pcg < 0)
+////	{
+////		maxit_pcg = 0;
+////	}
+////	Check for all zero right hand side vector => all zero solution
+////	n2b = norm(HTg(:));                     % Norm of rhs vector, b
+////	double n2b = 0.0;
+////	for (int i = 0; i < (M * cols); i++)
+////	{
+////		n2b = n2b + HTg[i][0] * HTg[i][0];
+////	}
+////	n2b = sqrt(n2b);
+////	if (n2b == 0)
+////	{
+////		flag_pcg = 0;
+////		iter_pcg = 0;
+////		for (int i = 0; i < (M * cols); i++)
+////		{
+////			X_pcg[i][0] = 0.0;
+////		}
+////		break;
+////	}
+////
+////	for (int i = 0; i < (M * cols); i++)
+////	{
+////		X_pcg[i][0] = fTemp[i][0];
+////	}
+////	Set up for the method
+////	flag_pcg = 1;
+////	double tolb_pcg = cg_tol * n2b;
+////	double normr_pcg = 0.0, normr_act_pcg;
+////	int imin_pcg = 0;
+////	for (int i = 0; i < (M * cols); i++)
+////	{
+////		xmin_pcg[i][0] = X_pcg[i][0];
+////	}
+////	 r = b - iterapp('mtimes',afun,atype,x,varargin{:});
+////	for (int i = 0; i < (M * cols); i++)
+////	{
+////		r_pcg[i][0] = HTg[i][0] - (Y_Model[i][0] * X_pcg[i][0]);
+////		normr_pcg = r_pcg[i][0] * r_pcg[i][0] + normr_pcg;
+////	}
+////	normr_pcg = sqrt(normr_pcg);
+////	normr_act_pcg = normr_pcg;
+////	 Initial guess is a good enough solution
+////	if (normr_pcg <= tolb_pcg)
+////	{
+////		flag_pcg = 0;
+////		iter_pcg = 0;
+////		break;
+////	}
+////	double normrmin_pcg = normr_pcg, rho_pcg;
+////	int stag_pcg = 0, moresteps_pcg = 0, maxmsteps_pcg, maxstagsteps_pcg;
+////	rho_pcg = 1.0;
+////	maxmsteps_pcg = 1 - (M * cols);
+////	if (maxmsteps_pcg > 0)
+////	{
+////		maxmsteps_pcg = 0;
+////	}
+////	maxstagsteps_pcg = 3;
+////	double pq_pcg, alpha_pcg = 0.0;
+////	loop over maxit iterations (unless convergence or failure)
+////	int rho1_pcg;
+////	double beta_pcg, normp_pcg, normx_pcg;
+////	int ii;
+////	for (ii = 0; ii < (M * cols); ii++)
+////	{
+////		for (int i = 0; i < (M * cols); i++)
+////		{
+////			y_pcg[i][0] = r_pcg[i][0];
+////			z_pcg[i][0] = y_pcg[i][0];
+////		}
+////		rho1_pcg = rho_pcg;
+////		if ((rho_pcg == 0) || isinf(rho_pcg))
+////		{
+////			flag_pcg = 4;
+////			break;
+////		}
+////
+////		if (ii == 0)
+////		{
+////			for (int i = 0; i < (M * cols); i++)
+////			{
+////				p_pcg[i][0] = z_pcg[i][0];
+////			}
+////		}
+////		else
+////		{
+////			beta_pcg = ((double)rho_pcg) / ((double)rho1_pcg);
+////			if ((beta_pcg == 0) || isinf(beta_pcg))
+////			{
+////				flag_pcg = 4;
+////				break;
+////			}
+////			for (int i = 0; i < (M * cols); i++)
+////			{
+////				p_pcg[i][0] = z_pcg[i][0] + beta_pcg * p_pcg[i][0];
+////			}
+////		}
+////		pq_pcg = 0.0;
+////		normp_pcg = 0.0;
+////		normx_pcg = 0.0;
+////		for (int i = 0; i < (M * cols); i++)
+////		{
+////			q_pcg[i][0] = (Y_Model[i][0] * p_pcg[i][0]);
+////			pq_pcg = q_pcg[i][0] * p_pcg[i][0] + pq_pcg;
+////			normp_pcg = p_pcg[i][0] * p_pcg[i][0] + normp_pcg;
+////			normx_pcg = normx_pcg + X_pcg[i][0] * X_pcg[i][0];
+////		}
+////		if ((pq_pcg <= 0) || isinf(pq_pcg))
+////		{
+////			flag_pcg = 4;
+////			break;
+////		}
+////		else
+////		{
+////			alpha_pcg = (double)rho_pcg / pq_pcg;
+////		}
+////		if (isinf(alpha_pcg))
+////		{
+////			flag_pcg = 4;
+////			break;
+////		}
+////
+////		 Check for stagnation of the method
+////		normp_pcg = sqrt(normp_pcg);
+////		normx_pcg = sqrt(normx_pcg);
+////		if (normp_pcg * fabs(alpha_pcg) < eps * normx_pcg)
+////		{
+////			stag_pcg += 1;
+////		}
+////		else
+////		{
+////			stag_pcg = 0;
+////		}
+////		form new iterate
+////		normr_pcg = 0.0;
+////		for (int i = 0; i < (M * cols); i++)
+////		{
+////			X_pcg[i][0] += alpha_pcg * p_pcg[i][0];
+////			r_pcg[i][0] = r_pcg[i][0] - alpha_pcg * q_pcg[i][0];
+////			normr_pcg += r_pcg[i][0] * r_pcg[i][0];
+////		}
+////		normr_pcg = sqrt(normr_pcg);
+////		normr_act_pcg = normr_pcg;
+////
+////		 check for convergence
+////
+////		if (normr_pcg <= tolb_pcg || stag_pcg >= maxstagsteps_pcg || moresteps_pcg)
+////		{
+////			r = b - iterapp('mtimes',afun,atype,x,varargin{:});
+////			normr_pcg = 0.0;
+////			for (int i = 0; i < (M * cols); i++)
+////			{
+////				r_pcg[i][0] = HTg[i][0] - (Y_Model[i][0] * X_pcg[i][0]);
+////				normr_pcg = r_pcg[i][0] * r_pcg[i][0] + normr_pcg;
+////			}
+////			normr_pcg = sqrt(normr_pcg);
+////			normr_act_pcg = normr_pcg;
+////			if (normr_act_pcg <= tolb_pcg)
+////			{
+////				flag_pcg = 0;
+////				iter_pcg = ii;
+////				break;
+////			}
+////			else
+////			{
+////				if (stag_pcg >= maxstagsteps_pcg && moresteps_pcg == 0)
+////				{
+////					stag_pcg = 0;
+////				}
+////				moresteps_pcg += 1;
+////				if (moresteps_pcg >= maxmsteps_pcg)
+////				{
+////					flag_pcg = 3;
+////					iter_pcg = ii;
+////					break;
+////				}
+////			}
+////		}
+////
+////		update minimal norm quantities
+////		if (normr_act_pcg < normrmin_pcg)
+////		{
+////			normrmin_pcg = normr_act_pcg;
+////			imin_pcg = ii;
+////			for (int i = 0; i < (M * cols); i++)
+////			{
+////				xmin_pcg[i][0] = X_pcg[i][0];
+////			}
+////
+////		}
+////		if (stag_pcg >= maxstagsteps_pcg)
+////		{
+////			flag_pcg = 3;
+////			break;
+////		}
+////
+////	}
+////	// returned solution is first with minimal residual
+////	double r_comp_pcg = 0.0;
+////	if (flag_pcg != 0)
+////	{
+////		for (int i = 0; i < (M * cols); i++)
+////		{
+////			r_comp_pcg += (HTg[i][0] - (Y_Model[i][0] * xmin_pcg[i][0])) * (HTg[i][0] - (Y_Model[i][0] * xmin_pcg[i][0]));
+////		}
+////		r_comp_pcg = sqrt(r_comp_pcg);
+////		if (r_comp_pcg <= normr_act_pcg)
+////		{
+////			for (int i = 0; i < (M * cols); i++)
+////			{
+////				X_pcg[i][0] = xmin_pcg[i][0];
+////			}
+////			iter_pcg = imin_pcg;
+////		}
+////		else
+////		{
+////			iter_pcg = ii;
+////		}
+////	}
+////}// fin PCG
+////printf("cg_tol = %f | iter = %d | flag = %d \n", cg_tol, iter_pcg, flag_pcg);
\ No newline at end of file