  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.
