[MatLab] Filter a tomographic image in Fourier’s space

MatLab has built-in functions to simulate acquisition and elaboration of tomographic (as in CT) images. When it comes to filtering the image prior to back-projecting it, it is possible to do it yourself without relying on the (good as in Shepp-Logan) filters MatLab has.

 

We will filter our image in Fourier’s space. For each column of the sinogram, we:

• apply the Fourier transform
• filter it
• apply the Fourier antitransform

When we reconstruct our image WITHOUT having MatLab apply any filter, we’ll see the image, filtered with our filter, as a result. Get the source code here.