Efficient InSAR phase noise reduction via total variation regularization

We consider the phase noise filtering problem for Interferometric Synthetic Aperture Radar (InSAR) using a total variation regularized complex linear least squares formulation. Although the original formulation is convex, solving it directly with the standard CVX package is time consuming due to the large problem size. In this paper, we introduce the effective and efficient alternating direction method of multipliers (ADMM) to solve the equivalent well-defined complex formulation for the real and imaginary parts of the optimization variables. Both the iteration complexity and the computational complexity of the ADMM are established in the forms of theorems for our InSAR phase noise problem. Simulation results based on simulated and measured data show that this new InSAR phase noise reduction method not only is 3 orders of magnitude faster than the standard CVX solver, but also has a much better performance than the several existing phase filtering methods.