Complex-valued image denosing based on group-wise complex-domain sparsity

TL;DR

This paper introduces new complex-domain filtering algorithms based on group-wise sparsity for phase imaging and wavefront reconstruction, addressing non-linear, non-Gaussian noise challenges with non-iterative and iterative methods.

Contribution

It proposes a novel class of complex domain filters utilizing group-wise sparsity, generalizing previous BM3D-based methods for improved phase and amplitude reconstruction.

Findings

Algorithms demonstrate high efficiency in simulations

Effective handling of non-Gaussian, signal-dependent noise

Generalization of existing BM3D-based techniques

Abstract

Phase imaging and wavefront reconstruction from noisy observations of complex exponent is a topic of this paper. It is a highly non-linear problem because the exponent is a 2{\pi}-periodic function of phase. The reconstruction of phase and amplitude is difficult. Even with an additive Gaussian noise in observations distributions of noisy components in phase and amplitude are signal dependent and non-Gaussian. Additional difficulties follow from a prior unknown correlation of phase and amplitude in real life scenarios. In this paper, we propose a new class of non-iterative and iterative complex domain filters based on group-wise sparsity in complex domain. This sparsity is based on the techniques implemented in Block-Matching 3D filtering (BM3D) and 3D/4D High-Order Singular Decomposition (HOSVD) exploited for spectrum design, analysis and filtering. The introduced algorithms are a generalization of the ideas used in the CD-BM3D algorithms presented in our previous publications. The algorithms are implemented as a MATLAB Toolbox. The efficiency of the algorithms is demonstrated by simulation tests.