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

Interferometric phase (InPhase) images, acquired by phase imaging systems, often suffer from two major degradations: 1) phase wrapping, caused by the sinusoidal $2\pi $ -periodic sensing mechanism, and 2) noise, introduced by the acquisition process or the system. This work focuses on InPhase denoising, which is a fundamental restoration step to many posterior applications of InPhase, namely to phase unwrapping. The presence of sharp fringes, which arises from phase wrapping, makes InPhase denoising a hard inverse problem. Motivated by the local sparsity often exhibited by InPhase images 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 counterpart, as well as other state-of-the-art InPhase denoising algorithms, is provided.