Image reconstruction for rectangular shapes in computed tomography

Abstract

Typical computed tomography reconstruction algorithms require the CT scanner to scan around the full 180 degrees of the object, discretizing the image reconstruction problem in order to make an approximation of the original image. We restrict the problem to the premise of non-overlapping rectangles forming the image and compute the exact Radon Transform of the image. Then the inverse problem is: given a certain number of projections, find the configuration of rectangles (of different sizes and orientations) which best match with the projection data. Given this assumption, a new algebraic method is developed. For larger problems (many projections of many rectangles), this method becomes computationally inefficient and instead a binary linear programming problem is formulated. Both methods require only a few CT scan measurements and produce accurate approximations of the original image.