Image reconstruction from noisy digital holograms

Abstract

The method of projection onto convex sets (POCS) is used in signal reconstruction to find a function that satisfies a collection of constraints, provided each of these constraints defines a convex set. If the constraints are inconsistent then a modified method of POCS may be used to find the fixed point of the POCS operator. This problem arises in the area of signal reconstruction from noisy multiple-frequency digital holograms, where it is required to compute a signal that satisfies known data subject to the constraint that it has a finite region of support. For noisy data there may exist no such signal and hence the constraint is inconsistent with the known data. Thus a modified POCS method needs to be applied. The paper reviews the method of image reconstruction from digital holograms. Two ways of applying the modified POCS method (called the PONICS method) are presented. Studies reported here show the effectiveness of the method for image reconstruction from noisy multiple-frequency holograms.