Filtered Back-Projection Reconstruction with Non-Uniformly Under-Sampled Projections

Tomographic imaging systems normally assume measurements with uniform angular sampling. The view angles are uniformly distributed, and the number of views is approximately the number of the detectors at one view. If the Nyquist sampling criterion is not satisfied, aliasing artifacts may appear in the reconstructed image. If the angular sampling is not uniform, we may be able to reconstruction the image using under-sampled sinograms. This paper presents a case study, which involves a non-uniformly under-sampled sinogram. A closed-form formula is proposed to convert the non-uniformly under-sampled sinogram to uniformly properly sampled sinogram. Finally, the filtered back-projection (FBP) algorithm is used to reconstruct the image. The proposed formula is exact in the sense that the sinogram is band-limited, which is never true in reality.