Towards Robustness and Efficiency of Coherence-Guided Complex Convolutional Sparse Coding for Interferometric Phase Restoration

Recently, complex convolutional sparse coding (ComCSC) has demonstrated its effectiveness in interferometric phase restoration, owing to its prominent performance in noise mitigation and detailed phase preservation. By incorporating the estimated coherence into ComCSC as prior knowledge for re-weighting individual complex residues, coherence-guided complex convolutional sparse coding (CoComCSC) further improves the quality of restored phases, especially over heterogeneous land-covers with rapidly varying coherence. However, due to the exploited $L_{2}$ norm of the data fidelity term, the original CoComCSC is not robust to outliers when relatively low coherence values are sparsely distributed over high ones. We propose CoComCSC-L1 and CoComCSC-Huber to improve the robustness of CoComCSC based on the $L_{1}$ and Huber norms. Moreover, we propose an efficient solver to decrease the computational cost of solving the linear system subproblem within ComCSC-based optimization problems. By comparing the proposed methods to other state-of-the-art methods using both simulated and real data, the proposed methods demonstrate their effectiveness. Additionally, the proposed solver has the potential to improve optimization speed by approximately 10% compared to the state-of-the-art solver.