New POCS algorithms for regularization of inverse problems (original) (raw)

Ill-posed problems described by first-kind Fredholm equations appear in many interesting practical cases in engineering or mathematical physics, such as deconvolution, and require regularization techniques to get adequate solutions. This paper presents, under a projection operators onto convex sets (POCS) framework to introduce the needed regularization operations, a series of non-adaptive and adaptive POCS regularization algorithms which offer as main advantages (besides including previously proposed methods) a lower computational load and the possibility of including any kind of constraints, linear and nonlinear. A series of simulation examples serve to appreciate the high performance of the proposed techniques in a typical problem: recovering the discontinuites of a sequence showing sharp edges.