A Phase Filter for Multi-Pass InSAR Stack Data by Hybrid Tensor Rank Representation

Multi-pass synthetic aperture radar interferometry (InSAR) stack data denoising is a significant prerequisite for extracting geophysical parameters. InSAR stack data can be considered as a third-order tensor in the complex domain, and the process of tensor decomposition to acquire the low-rank tensor has been employed as an effective interferometric phase filter for InSAR stack data. It is noted that the definition of tensor rank is the core of tensor-based filter. In this paper, we investigate the properties of Tucker rank, CANDECAMP/PARAFAC (CP) rank and Kronecker Basis Representation (KBR) in InSAR stack data, and then we found that it is suitable to extend KBR, as a hybrid tensor rank representation, into InSAR tensor filtering. Firstly, an improved InSAR phase tensor model is utilized to represent the phenomenon of interferometric phase, which perceives the observed InSAR phase tensor as the combination of low-rank, sparse noise and Gaussian noise tensors. Based on the principle of KBR, then the novel phase filtering method, named as KBR-InSAR, is proposed to decompose the complex InSAR tensor supported by the improved InSAR phase tensor model. With the comparison of other tensor filters, i.e. HoRPCA and WHoRPCA and the widespread traditional filters operating on a single interferometric pair, e.g. Goldstein, NL-SAR, NL-InSAR and InSAR-BM3D, it can be proved that the KBR-InSAR can efficiently reduce the noise with superior fringes preservation in the experiments on the simulated and real InSAR stack data collected from Sentinel-1B.