Why iradon returns negative pixel values?

Question

I took 200 projections at a step angle of 1.8 degrees using LabVIEW software. The size of the image is 2748 x 2748 pixels, uint16. Then using Matlab, I load the projection images, do the flat field correction, resize the image by 1/3 and save the images as .mat file. Then I run the code below for the filtered backprojection.

interp='linear'; %set interpolation: nearest, linear, spline, pchip, v5cubic
filter='Hann'; %set filter: Ram-Lak, Shepp-Logan, Cosine, Hamming, Hann, None

for s=1:916

   for i=1:200
   a(i,:)=proj065(:,s,i);
   end
   a=a';
   %figure(3), imagesc(a)
   b=iradon(a,1.8,interp,filter);
   imagesc(b);
   recon(:,:,s)=b;
   s
   clear a
end

If I used a filter in this code, I will get negative pixel values.

But, if I run the code without the filter, I will get positive pixel values.

Any idea why iradon returns negative pixel values in filtered back projection?

Thank you.

Nurul

Answer 1

Yes, the FBP (filtered back-projection) algorithm will do that. It can wrongly reconstruct voxels as having negative values, due to noise and discretization on the data. Nothing you can do about it than just crop those values generally.

As my PhD is about tomography reconstruction algorithms I feel contractually obligated (joking) to suggest the use of iterative algorithms to possibly obtain better images (never worse, often considerably better). Check SART/SIRT or CGLS for this problem.

However, you are calling your function wrong! In tomography, the step size is not enough to reconstruct an image, you generally need the exact angles, thus iradon doesnt accept a step size as an input, it accepts an array of angles.

in your case, theta should be theta=linspace(0,360-200/360,200), and you should call iradon(a,theta,...)