  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 paper, we propose an alternative
approach for InSAR phase restoration, i.e. Complex Convolutional Sparse Coding
(ComCSC) and its gradient regularized version. To our best 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 of the elementary phase
components for the interferometric phases. The experimental results on
synthetic and realistic high- and medium-resolution datasets 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 paper will be made publicly available for reproducible
research inside the community.
