Image reconstruction in tomography using convex projections

Abstract

The method of projections onto convex sets (POCS) has been widely used in image recovery and synthesis problems but it has never been used as an actual reconstruction algorithm in tomography. Yet POCS offers certain advantages over methods such as convolution backprojection or direct Fourier inversion. What are these advantages? First, POCS does not require a particular data gathering geometry (e.g., parallel beam or fan beam projections); it can be used with any arbitrary set of projection data. Second, POCS furnishes a systematic technique for incorporating a priori information about the image. It is interesting to note that when POCS is used in its most primitive mode, i.e., the only constraints are those imposed by the line-integral projections, it becomes the well-known ART algorithm. We describe how POCS is used to reconstruct images in tomography and present computer simulations to verify the feasibility of the procedure.