Sparse Regularization of Interferometric Phase and Amplitude for InSAR Image Formation Based on Bayesian Representation

Interferometric synthetic aperture radar (InSAR) images are corrupted by strong noise, including interferometric phase and speckle noises. In general, the scenes in homogeneous areas are characterized by continuous-variation heights and stationary backscattered coefficients, exhibiting a locally spatial stationarity. The stationarity provides a rational of sparse representation of amplitude and interferometric phase to perform noise reduction. In this paper, we develop a novel algorithm of InSAR image formation from Bayesian perspective to perform interferometric phase noise reduction and despeckling. In the scheme, the InSAR image formation is constructed via maximum a posteriori estimation, which is formulated as a sparse regularization of amplitude and interferometric phase in the wavelet domain. Furthermore, the statistics of the wavelet-transformed image is modeled as complex Laplace distribution to enforce a sparse prior. Then, multichannel imaging is realized using a modified quasi-Newton method in a sequential and iterative manner, where both the interferometric phase and speckle noises are reduced step by step. Due to the simultaneously sparse regularized reconstruction of amplitude and interferometric phase, the performance of noise reduction can be effectively improved. Then, we extend it to joint sparse constraint on multichannel data by considering the joint statistics of multichannel data. Finally, experimental results based on simulated and measured data confirm the effectiveness of the proposed algorithm.