A new flexible 2D-image reconstruction in computed tomography based on non-uniform sampling theorem for spatially band-limited signals

Abstract

After a brief review of the ordinary sampling theorem for bandlimited signals, the non-uniform sampling theorem is given, together with the condition for no aliasing error being made clear. Based on the fundamentals, a new flexible method of 2D-image reconstruction from restricted projection data in computed tomography is proposed, that can flexibly reconstruct the precise 2D-images from broad kinds of nonuniform projections collected speedily without any explicit 1D/2D-interpolation of data or image restoration techniques. The principle as well as the effectiveness of the proposed method are confirmed through numerical experiments with assumed distributions of absorption rates about objects in computed X-ray tomography.