Efficient InSAR Phase Noise Reduction via Compressive Sensing in the Complex Domain

Two novel phase noise filtering algorithms for interferometric synthetic aperture radar (InSAR) are presented in this paper. Aiming at the nonlocal high self-similarity existing in the InSAR phase, we establish the phase noise filtering formulations with the ℓ
₀
-norm regularizer and the ℓ
₁
-norm regularizer, respectively. Although these two original formulations are nonconvex, we attempt to solve them by successive upper bound minimization combined with dictionary learning method. Specifically, for the noise reduction formulation with the ℓ
₀
-norm regularizer, we first divide the original problem into a series of decoupled subproblems. Second, we obtain the approximate subproblem, which is locally tight upper bound of each subproblem by using a majorization- minimization technique. Third, we compute the sparse parameter vector for each approximate subproblem, followed by a matrix form update for the dictionary. The three steps are tackled cyclically until a satisfying solution is attained. The noise reduction problem with the ℓ
₁
-norm regularizer is handled in a similar approach. We also establish the computational complexities of these two methods and summarize their distinct performance. Simulation results based on both synthetic data and simulated InAR data show that these two new InSAR phase noise reduction methods have much better performance than several existing phase filtering methods.