Learning Convolutional Sparse Coding on Complex Domain for Interferometric Phase Restoration

Interferometric phase restoration has been investigated for decades and most of the state-of-the-art methods have achieved promising performances for InSAR phase restoration. These methods generally follow the nonlocal filtering processing chain, aiming at circumventing the staircase effect and preserving the details of phase variations. In this article, we propose an alternative approach for InSAR phase restoration, that is, Complex Convolutional Sparse Coding (ComCSC) and its gradient regularized version. To the best of the authors' knowledge, this is the first time that we solve the InSAR phase restoration problem in a deconvolutional fashion. The proposed methods can not only suppress interferometric phase noise, but also avoid the staircase effect and preserve the details. Furthermore, they provide an insight into the elementary phase components for the interferometric phases. The experimental results on synthetic and realistic high- and medium-resolution data sets from TerraSAR-X StripMap and Sentinel-1 interferometric wide swath mode, respectively, show that our method outperforms those previous state-of-the-art methods based on nonlocal InSAR filters, particularly the state-of-the-art method: InSAR-BM3D. The source code of this article will be made publicly available for reproducible research inside the community.