This is a code for Fourier reconstruction of a Shepp-Logan phantom model.

In section % Compute 2D Fourier transform of 1D Fourier transform data, the line F_2d = F_2d + F_1d * exp(-2i * pi * (u * cosd(theta(n)) + v * sind(theta(n)))); yields an error due to incompatible dimensions for matrix multiplication. The aim of this line is to add fourier coefficients into the 2D fourier space.

Please help:

- Improve the code and troubleshoot error above

- Show image of original & reconstructed image side by side

- Assess effect of projection sampling density & range

- Additionally, compare different filters

Code:

% Load Shepp-Logan phantom model

phantom_image = phantom('Modified Shepp-Logan', 256);

% Set up parameters

num_angles = 180;

num_samples = 256;

% Generate projection angles

theta = linspace(0, 179, num_angles);

% Compute Radon transform

radon_transform = radon(phantom_image, theta);

% Compute 1D Fourier transform of Radon transform along s direction

f_1d = fft(radon_transform);

% Create grid for 2D Fourier transform

u = linspace(-1, 1, num_samples);

[v, u] = meshgrid(u);

% Compute 2D Fourier transform of 1D Fourier transform data

F_2d = zeros(num_samples);

for n = 1:num_angles

F_1d = f_1d(:, n);

F_2d = F_2d + F_1d * exp(-2i * pi * (u * cosd(theta(n)) + v * sind(theta(n))));

end

% Interpolate coordinate system using gridata function

[X, Y] = meshgrid(1:num_samples);

[Xq, Yq] = meshgrid(linspace(1, num_samples, 512));

reconstructed_image = griddata(X, Y, abs(ifft2(F_2d)), Xq, Yq, 'cubic');

% Display original and reconstructed images

subplot(1, 2, 1);

imshow(phantom_image);

title('Original Image');

subplot(1, 2, 2);

imshow(reconstructed_image);

title('Reconstructed Image');