Phase imaging via sparse coding in the complex domain based on high-order svd and nonlocal BM3D techniques

The paper addresses interferometric phase image estimation, that is, the estimation of phase modulo-2π images from sinusoidal 2π-periodic and noisy observations. These degradation mechanisms make interferometric phase image estimation a challenging problem. We tackle this challenge by reformulating the true estimation problem as a sparse regression in the complex domain. Following the standard procedure in patch-based image restoration, the image is partitioned into small overlapping square patches. BM3D algorithm equipped with high order SVD (HOSVD) is used to form complex domain frames suitable to sparse representations of the complex-valued data. HOSVD applied to the groups of BM3D data enables the design of spatially variant and data adaptive orthonormal complex domain transforms. The effectiveness of the new sparse coding based approach to interferometric phase estimation, termed Interferometric PHASE via Block matching and High order SVD (InPHASE-BHS) is illustrated in a series of simulation experiments where it outperforms the state-of-the-art.