SURE-Fuse WFF: A Multi-Resolution Windowed Fourier Analysis for Interferometric Phase Denoising

Abstract

Interferometric phase (InPhase) imaging is an important part of many present-day coherent imaging technologies. Often in such imaging techniques, the acquired images, known as interferograms, suffer from two major degradations: 1) phase wrapping caused by the fact that the sensing mechanism can only measure sinusoidal 2π-periodic functions of the actual phase, and 2) noise introduced by the acquisition process or the system. This work focusses on InPhase denoising which is a fundamental restoration step to many posterior applications of InPhase, namely to phase unwrapping. The presence of sharp fringes that arises from phase wrapping makes InPhase denoising a hard-inverse problem. Motivated by the fact that the InPhase images are often locally sparse in Fourier domain, we propose a multi-resolution windowed Fourier filtering (WFF) analysis that fuses WFF estimates with different resolutions, thus overcoming the WFF fixed resolution limitation. The proposed fusion relies on an unbiased estimate of the mean square error derived using the Stein's lemma adapted to complex-valued signals. This estimate, known as SURE, is minimized using an optimization framework to obtain the fusion weights. Strong experimental evidence, using synthetic and real (InSAR & MRI) data, that the developed algorithm, termed as SURE-fuse WFF, outperforms the best hand-tuned fixed resolution WFF as well as other state-of-the-art InPhase denoising algorithms, is provided.

Comparative study of phase unwrapping algorithms based on solving the Poisson equation

“…Overall, the iterative methods, especially the TIE-FD-DCT-based method, are recommended to be used in the actual applications. However, the performance of the iterative methods was not so satisfactory under a very heavy noise condition (as shown in figures 8(c6)-(d6)), a weighting [81][82][83] or pre-filtering [37,[84][85][86][87][88][89] strategy can be adopted to further improve the performance of those methods. Besides, with a booming development of deep learning [90][91][92][93][94][95][96][97], using a proper network to enhance or accomplish the phase unwrapping is also a promising research direction.…”

Class-Specific Interferometric Phase Estimation Using Patch-Based Importance Sampling

“…Although WFF yields state-of-the-art PD performance in many InPhase applications, it is limited by its fixed-resolution due to the lack of an adaptive window. SURE-fuse WFF [37] is a recent PD algorithm, based on a multi-resolution WFF analysis to overcome the fixed-resolution limitations of the original WFF. In that algorithm, the WFF estimates having different resolutions are fused in a linear, pixel-wise, and data-adaptive manner by minimizing an unbiased estimate of the mean square error derived using Stein's lemma.…”