Interferometric Phase Image Estimation via Sparse Coding in the Complex Domain

Abstract

This paper addresses interferometric phase image estimation, i.e., the estimation of phase modulo-2π images from sinusoidal 2π-periodic and noisy observations. These degradation mechanisms make interferometric phase image estimation a quite challenging problem. We tackle this challenge by reformulating the true estimation problem as a sparse regression, often termed sparse coding, in the complex domain. Following the standard procedure in patch-based image restoration, the image is partitioned into small overlapping square patches, and the vector corresponding to each patch is modeled as a sparse linear combination of vectors, termed the atoms, taken from a set called dictionary. Aiming at optimal sparse representations, and thus at optimal noise removing capabilities, the dictionary is learned from the data that it represents via matrix factorization with sparsity constraints on the code (i.e., the regression coefficients) enforced by the 1 norm. The effectiveness of the new sparse-coding-based approach to interferometric phase estimation, termed the SpInPHASE, is illustrated in a series of experiments with simulated and real data where it outperforms the state-of-the-art.Index Terms-Dictionary learning (DL), image similarity, interferometric phase estimation, online learning, phase estimation, phase unwrapping, sparse regression.

New SAR Interferogram denoising method via sparse recovery based on L0 norm

“…note that more details about the relationship between the noise variance and the estimaton error threshold is given in (Hongxing et al, 2013). For the filtering results, we notice that the proposed approach reduce noise inside fringes very well.…”

Sparse‐coding denoising applied to reversible conformational switching of a porphyrin self‐assembled monolayer induced by scanning tunnelling microscopy

“…To find an approximated solution, we follow the same approach as in Hongxing et al . (), and choose the orthogonal basis pursuit (Pati et al ., ) algorithm because of its lower computational complexity compared with the others (Tibshirani, ; Chen et al ., ; Blumensath & Davies, ; Foucart, ; Vila & Schniter, ). The details can be found in (Hongxing et al ., ).…”

“…These parameters determine the reconstruction error and the noise attenuation of patch : although very small values of MNA, for example 1 or 2 atoms, are not enough to correctly represent data, a larger number gives more flexibility and adaptability and thus less noise reduction. The implementation of algorithm (Hongxing et al ., ) searches for the smallest number of atoms that attain an error less than δ, with at most the MNA. Note that the MNA is a hard threshold, i.e.…”

Complex domain nonlocal block-matching denoising based on high-order singular value decomposition (HOSVD)

“…The main problem of this development is a design of complex-valued bases enabling the sparsity in the complex domain. It was done in two different ways: the SpInPhase algorithm is based on complex domain dictionary learning with internal and external dictionaries [6] and the BM3D based algorithm uses HighOrder Singular Value Decomposition (HOSVD) [7], [8].…”