Question

Index in position 1 is invalid. Array indices must be positive integers or logical values.

Answer 1

Answer:

clc;

close all;

clear;

% The radon transform of Circle Phantom

PD=phantom('Modified Shepp-Logan');

% pad the image with zeros

padimage = [2,2];

PD= padarray(PD,padimage);

% Original image

subplot(2,3,1)

imagesc(PD);

colormap('gray');

title('Circle Phantom')

xlabel('X')

ylabel('Y')

% Theta is 0:180 with the increment of 0.5 degrees

freq = 2;

thetas = 0:freq:180;

% compute sinogram / radon transformation

gtheta = length(thetas);

gl = size(PD,1);

sinogram = zeros(gl,gtheta);

% loop for the number of angles

for i = 1:length(thetas)

tmpImage = imrotate(PD,-thetas(i),'bilinear','crop');

sinogram(:,i) = sum(tmpImage);

end

subplot(2,3,2)

imagesc(sinogram);

title('Circle Sinogram');

xlabel('l');

ylabel('\theta');

% The inverse radon transform with only 1 back projection that is theta = 0

thetas=0;

Fl = size(sinogram,1);

Ftheta = length(thetas);

% convert thetas to radians

thetas = (pi/180)*thetas;

% set up the backprojected image

g0 = zeros(Fl,Fl);

% find the middle index of the projections

Fmid = ceil(Fl/2);

% set up the coords of the image

[x,y] = meshgrid(ceil(-Fl/2):ceil(Fl/2-1));

% loop over each projection

for i = 1:Ftheta

% Using the back projection formula

rotCoords = Fmid+round(x*sin(thetas(i)) + y*cos(thetas(i)));

% % check which coords are in bounds

% indices = find((rotCoords > 0) & (rotCoords <= Fl));

% newCoords = rotCoords(indices);

% summation

rotCoords=floor(abs(rotCoords));

g0 = g0 + sinogram(rotCoords,i)./Ftheta;

end

subplot(2,3,3);

imagesc(g0);

title('Simple backprojection')

xlabel('X')

ylabel('Y')

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