Gerchberg-Type Linear Deconvolution And Extrapolation Algorithms
Robert J. Marks, David Keith Smith · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1984
Gerchberg's iterative extrapolation algorithm is generalized to two dimensions in two distinct ways. The first generalization is implemented on a coherent optical processor. Fundamental limitations are discussed. A second generalization is reformulated discretely and placed in closed form. A number of digital implementations are presented. A generalized methodology is then developed for a certain class of deconvolution problems. Gerchberg's algorithm and other deconvolution algorithms are shown to be special cases. Algorithm convergence and stability (posedness) are discussed and exemplified. Last, methods of incorporating further object information into the iterative algorithms are explored.