Abstract
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.
Highlights
Multi-pass synthetic aperture radar interferometry (InSAR) technique has gained a great achievement on elevation inversion [1] and deformation monitoring [2] by processing InSAR stack data
WHORPCA FOR InSAR TENSOR FILTERING The convex optimization algorithm in higher order RPCA (HoRPCA) satisfies the requirement of low-rank tensor recovery under most circumstances, but it is subject to the existence of high outlier ratio in the observed InSAR tensor
AND ANALYSIS we present and analyze the quantitative and qualitative results to prove the effectiveness of Kronecker Basis Representation (KBR)-InSAR
Summary
Multi-pass synthetic aperture radar interferometry (InSAR) technique has gained a great achievement on elevation inversion [1] and deformation monitoring [2] by processing InSAR stack data. Y. You et al.: Phase Filter for Multi-Pass InSAR Stack Data by Hybrid Tensor Rank Representation and that has a good performance in most cases. The phase filtering approaches based on tensor decomposition effectively restore the interferograms by using the entire InSAR stack data [16], [17]. InSAR stack data conforms to the mathematical representation of tensor and it has a low rank structure. HoRPCA is first applied to interferometric phase filtering by Kang et al [16], as an effective denoising step in the framework of ground displacement time-series recovery In this method, InSAR stack data modeled as a tensor can be decomposed into low rank tensor and outlier tensor (i.e. noise in InSAR stack data). Some symbols used in the paper are explained as follows. denotes element-wise product. ◦ denotes the vector outer product. ×n denotes n-mode product, which represents the product of tensor and matrix
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