Complex-valued image denosing based on group-wise complex-domain sparsity
This work addresses phase imaging and wavefront reconstruction for applications like optics or imaging, but it is incremental as it generalizes prior CD-BM3D algorithms.
The paper tackles the problem of phase and amplitude reconstruction from noisy complex-valued observations, which is highly non-linear and involves signal-dependent non-Gaussian noise. It proposes non-iterative and iterative complex domain filters based on group-wise sparsity, demonstrating efficiency through simulation tests.
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 2π-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.