Efficient noise reduction for interferometric phase image via non-local non-convex low-rank regularisation

This study considers the phase noise filtering problem for interferometric phase image using sparse optimisation technique. Since the original model can be formulated as a rank minimisation problem, it is difficult to solve. One appealing approach is to use a nuclear norm (NN) regularisation to relax the rank regulariser. However, the performance of such approach is not satisfying. In this study, the authors propose to use reweighted NN regularisation to approximate the rank regulariser, which leads to the low-rank reformulation. Though this reformulation is nonconvex, a new algorithm termed as spatially adaptive iterative weighted singular-value thresholding algorithm is proposed to effectively solve it. Specifically, the weight and image variables are updated alternatively by block coordinate descent iteration scheme. In addition, the corresponding computational complexity of the algorithm has been established. Simulation results based on simulated and measured data show that this new phase noise reduction method has much better performance than several existing phase filtering methods.