CODEWITHSUNDEEP
matlabgridffttomography-reconstruction
Anonymous
Anonymous

Reputation: 167

Direct 2D FFT from sinogram. Polar to cartesian grid interpolation in Matlab

In the theory of tomography imaging a sinogram is recorderded, which is series of projections at different angles of the sample. Taking FFT of this projections gives a slice in polar coordinates of the sample in the frequency space.

The command [X,Y] = pol2cart(THETA,RHO) will not do it automatically. So, how is the polar to cartesian grid interpolation implemented numerically in 2D in Matlab?

Upvotes: 0

Views: 1419

Answers (2)

lxg
lxg

Reputation: 226

The function [X,Y] = pol2cart(THETA,RHO) only performs the coordinate value conversion, i.e., X = RHO * cos(THETA) and Y = RHO * sin(THETA). However, what you need is the conversion of the data array, thus pol2cart() can do nothing to your problem.

You can refer to the function interp2(). On the other hand, since this problem is the interpolation with COMPLEX data, I am NOT sure whether interp2() could do the job directly. I also need the theory for complex interpolation.

Upvotes: 1

tashuhka
tashuhka

Reputation: 5126

You need to do a phase transformation:

theta = 0:0.1:2*pi;
rho = linspace(0,1,numel(theta));
[x,y] = pol2cart(-theta+pi/2,rho);

figure;
subplot(1,2,1);
polar(theta,rho);
subplot(1,2,2);
plot(y,x);
axis([-1 1 -1 1]);
grid on;

enter image description here

Upvotes: 2

Related Questions