POCS: a uniform framework for iterative image reconstruction algorithms

The theory of projection onto convex sets (POCS) is very useful for comparing iterative reconstruction algorithms. Although originally developed with the Euclidian distance, it has been shown that POCS can be attended to pseudo-distances or can even use a different distance for each convex set. Five well known iterative algorithms that can be used to reconstruct images from partial noisy data have been formulated by POCS. Additional convex constraints and relaxation parameters can thus be introduced in these algorithms.