Want to check the program is technically right and work accurately?

I have two signals, T_para and T_per (5*17*20) loaded from directory, I coded this program to do the following tasks:
Calculate the cost function
Apply interpolation to increase the density of a and r
Minimize the cost function using optimiztion method (Grid search method)
Plot figures with minimum cost value
Please check if there is a mistake technically or in the structure. My program code is:
clear all; clc; close all;
cloud = ‘Homo’;
T_para = zeros(5, 17, 20);
T_per = zeros(5, 17, 20);

% Initialize matrices
T_para_noisy = zeros(5, 17, 20);
T_per_noisy = zeros(5, 17, 20);

% Function to add AWGN
add_noise = @(signal, snr) awgn(signal, snr, ‘measured’);

% Define the cost function
% cost_function = @(original, noisy) sum((original(:) – noisy(:)).^2) / numel(original);
cost_function = @(original, noisy, variance) sum(((original(:) – noisy(:))./ (var(original(:)))).^2);

% Initialize arrays to store the optimal values and global minimum cost
lookup_table = [];
lookup_table_interp = [];

% Initialize global minimum cost values
global_min_cost = Inf;
optimal_a= 0;
optimal_r = 0;

% Define ranges for a and r
a_range = 0.01:0.01:0.05;
r_range = 4:20;

% Initialize cost matrix to store costs for all combinations of a and r
cost_matrix = zeros(length(a_range), length(r_range));

for h = 1000:1000:4000
for fov = [0.2, 0.5, 1, 2, 5, 10]

for a_idx = 1:length(a_range)
for r_idx = 1:length(r_range)
a = a_range(a_idx);
r = r_range(r_idx);

load([‘./Tabledata_’, cloud, ‘/’, num2str(h), ‘m-‘, num2str(fov), ‘mrad/TABLE.mat’]);

% Add noise to the signals
T_para_noisy = add_noise(T_para, 30); % 20dB SNR
T_per_noisy = add_noise(T_per, 30);

% Calculate the variance of the original signals
var_T_para = var(T_para, 0, ‘all’);
var_T_per = var(T_per, 0, ‘all’);

% Calculate the cost for each pair of original and noisy signals
cost_para = cost_function(T_para, T_para_noisy, var_T_para);
cost_per = cost_function(T_per, T_per_noisy, var_T_per);

% Sum the costs
total_cost = cost_para + cost_per;

% Store the cost for plotting
cost_matrix(a_idx, r_idx) = total_cost;

% Check if this is the new global minimum
if total_cost < global_min_cost
global_min_cost= total_cost;
optimal_a = a;
optimal_r = r;
end

end
end
% Store the optimal values and global minimum cost in the lookup table
lookup_table = [lookup_table; optimal_a, optimal_r, global_min_cost];

end
end

% Save and display the look-up table for optimal interpolated values
save(‘LookupTable.mat’, ‘lookup_table’);

% Initialize global minimum cost for interpolated values
global_min_cost_interp = Inf;
optimal_a_interp = 0;
optimal_r_interp = 0;

% Define finer gridded interpolant for cost_matrix
a_interp = 0.01:0.001:0.05;
r_interp = 4:0.5:20;

% Define the original and interpolated grids
[a_grid, r_grid] = meshgrid(a_range, r_range);
[a_interp_grid, r_interp_grid] = meshgrid(a_interp, r_interp);

% Transpose the cost_matrix to match the grid dimensions
cost_matrix = cost_matrix’;

% Apply gridded interpolation using spline method
cost_matrix_interp = interp2(a_grid, r_grid, cost_matrix, a_interp_grid, r_interp_grid, ‘spline’);

% Loop through the interpolated grid to find the global minimum
for a_interp_idx = 1:length(a_interp)
for r_interp_idx = 1:length(r_interp)
interpolated_cost = cost_matrix_interp(r_interp_idx, a_interp_idx); % Note the order of indices
% Check if this is the new global minimum
if interpolated_cost < global_min_cost_interp
global_min_cost_interp = interpolated_cost;
optimal_a_interp = a_interp(a_interp_idx);
optimal_r_interp = r_interp(r_interp_idx);
end
end
end

% Add to the lookup table
lookup_table_interp = [lookup_table_interp; optimal_a_interp, optimal_r_interp, global_min_cost_interp];

% Save and display the look-up table for optimal interpolated values
save(‘LookupTable_Interp.mat’, ‘lookup_table_interp’);

disp(‘Global minimum interpolated cost:’);
disp(global_min_cost_interp);

% Normalize the cost_matrix_interp values
min_cost = min(cost_matrix_interp(:));
max_cost = max(cost_matrix_interp(:));
normalized_cost_matrix_interp = (cost_matrix_interp – min_cost) / (max_cost – min_cost);

%%
% Plot the normalized interpolated cost function
figure(1);
surf(a_interp_grid, r_interp_grid, cost_matrix_interp);
shading interp;
colormap parula;
colorbar;
set(gca, ‘color’, ‘w’, ‘FontSize’, 12, ‘LineWidth’, 1, ‘FontWeight’, ‘normal’);
ylabel(‘R_{e} interp (mum)’);
xlabel(‘alpha_{e} interp (m^{-1})’);
zlabel(‘Normalized interpolated cost function’);
title(‘Normalized interpolated CF over alpha_{e} interp and R_{e} interp’);
set(gca, ‘box’, ‘on’, ‘LineWidth’, 1, ‘FontName’, ‘Arial’, ‘FontSmoothing’, ‘on’);
set(gca, ‘xlim’, [0.01 0.05], ‘xtick’, [0.01 0.02 0.03 0.04 0.05], ‘ylim’, [4 20], ‘ytick’, [4 8 12 16 20]);
grid on;
hold on;

% Create a meshgrid for plotting
[A, R] = meshgrid(a_interp, r_interp);

% Reshape the matrices to vectors for plotting
A_vector = reshape(A, [], 1);
R_vector = reshape(R, [], 1);
Re_cost_matrix_interp = reshape(cost_matrix_interp, [], 1);

% Find the global minimum in the interpolated cost matrix
[global_min_cost_interp, min_idx] = min(Re_cost_matrix_interp);
optimal_a_interp = A_vector(min_idx);
optimal_r_interp = R_vector(min_idx);

% Mark the minimum point
hold on;
surf_handle=plot3(optimal_a_interp, optimal_r_interp, global_min_cost_interp, ‘ro’, ‘MarkerSize’, 12, ‘MarkerFaceColor’, ‘r’);
view(3); % Set the viewing angle to 3D
% Bring the red point to the front
uistack(surf_handle, ‘top’); % Bring the red point to the front
hold off;

% Plot the 2D Contour Plot of the interpolated cost function
figure(2);
contourf(a_interp_grid, r_interp_grid, normalized_cost_matrix_interp, 20);
colorbar;
xlabel(‘alpha_{e} interp (m^{-1})’);
ylabel(‘R_{e} interp (mum)’);
title(‘2D Contour Plot of interpolated normalized CF’);
set(gca,’FontSize’, 12, ‘LineWidth’, 1, ‘FontWeight’, ‘normal’);
set(gca, ‘box’, ‘on’, ‘LineWidth’, 1, ‘FontName’, ‘Arial’, ‘FontSmoothing’, ‘on’);
set(gca, ‘xlim’, [0.01 0.05], ‘xtick’, [0.01 0.02 0.03 0.04 0.05], ‘ylim’, [4 20], ‘ytick’, [4 8 12 16 20]);
hold on;
plot(optimal_a_interp, optimal_r_interp, ‘ro’, ‘MarkerSize’, 12, ‘MarkerFaceColor’, ‘r’); % Mark the minimum point from interpolated grid search
% plot(optimal_a, optimal_r, ‘bo’, ‘MarkerSize’, 10, ‘LineWidth’, 2); % Mark the minimum point from original grid search
hold off;

% Plot the normalized cost values
figure(3);
scatter3(R_vector, A_vector, Re_cost_matrix_interp, ‘filled’);
xlabel(‘R_{e} interp (mum)’);
ylabel(‘alpha_{e} interp (m^{-1})’);
zlabel(‘Interpolated cost function’);
title(‘Normalized interpolated CF over alpha_{e} interp and R_{e} interp’);
set(gca, ‘color’, ‘w’, ‘FontSize’, 12, ‘LineWidth’, 1, ‘FontWeight’, ‘normal’);
set(gca, ‘box’, ‘on’, ‘FontName’, ‘Arial’, ‘FontSmoothing’, ‘on’);
set(gca, ‘ylim’, [0.01 0.05], ‘ytick’, [0.01 0.02 0.03 0.04 0.05], ‘xlim’, [4 20], ‘xtick’, [4 8 12 16 20]);
grid on;

hold on;

% Set the view angle
view(60, 40); % Adjust the view angles to see the plot clearly
% Mark the minimum point with a circle
surf_handle = plot3(optimal_r_interp, optimal_a_interp, global_min_cost_interp, ‘ro’, ‘MarkerSize’, 12, ‘MarkerFaceColor’, ‘r’);

% Bring the red point to the front
uistack(surf_handle, ‘top’); % Bring the red point to the front
hold off;I have two signals, T_para and T_per (5*17*20) loaded from directory, I coded this program to do the following tasks:
Calculate the cost function
Apply interpolation to increase the density of a and r
Minimize the cost function using optimiztion method (Grid search method)
Plot figures with minimum cost value
Please check if there is a mistake technically or in the structure. My program code is:
clear all; clc; close all;
cloud = ‘Homo’;
T_para = zeros(5, 17, 20);
T_per = zeros(5, 17, 20);