using discrete FT with iradon

Dear all,

according to the matlab documentation:

'iradon uses the filtered back-projection algorithm to perform the inverse Radon transform. The filter is designed directly in the frequency domain and then multiplied by the FFT of the projections.'

I want however to try and do the procedure using discrete FT and not fast FT. Does anyone know of how to do this?

Thanks

Matt

Answer 1

[Steve Eddins]

Fast Fourier transform, or FFT, refers to a family of fast algorithms for computing the discrete Fourier transform, or DFT. See these blog posts for information about different kinds of Fourier transforms and the relationships between them.

[Matthew O'Brien]

Hi Steve, thanks for the information. I will take a look. The reason i asked the question is that i am trying to perform and inverse radon transform of some data and i get a very different result from a program which claims to perform a full DFT and matlab which i know uses FFT to calculate the DFT. Effectively the matlab iradon command results in a strong 'halo' around the image not present in the other programs reconstruction.

have you heard of problems like this before?

Thanks

Matt

[Steve Eddins]

No. You could try the different filtering and interpolation options with iradon. However, the idea that there is a difference between a "full DFT" and what the MATLAB fft function calculates is simply incorrect.

[Matthew O'Brien]

Hi Steve, I have identified the problem and as you say it has nothing to do with DFT and FFT. Effectively the issue is that the sinogram data i have has a constant 'background' and the actual data is very low compared to this. I can recreate the problem by simply creating a Matrix of 1's which represent the 'sinogram' if this is then inverse radon transformed you get the ring:

sino = ones(20,20);

out = iradon(sino,[],20)

imagesc(out(1:20,1:20)); figure(gcf)

I guess this is a mathematical consequence of trying to perform iradon on data which doesnt contain a real sinogram?