Image Reconstruction by the Method of Convex Projections

Abstract

: In medical imaging modality, such as X-ray computerized tomography (CT) and positron emission tomography (PET), image reconstruction from projection is to produce an image of a two dimensional object from its line integrals along a finite number of lines. Given some subsets of a priori knowledge about the problem in Hilbert space, a formalized problem is to find the object from observed vector. If the subsets are closed and convex sets, given the convex projections onto the sets, the problem can be solved by using the method of projections onto convex sets (POCS). In this paper, we apply the method of projection onto convex sets to image reconstruction problems and evaluate the image quality in computer simulations. Also, we evaluate the influence of the noise in reconstructed image.