The filtering of multi-pass synthetic aperture radar interferometry (InSAR) stack data is a necessary preprocessing step utilized to improve the accuracy of the object-based three-dimensional information inversion in urban area. InSAR stack data is composed of multi-temporal homogeneous data, which is regarded as a third-order tensor. The InSAR tensor can be filtered by data fusion, i.e., tensor decomposition, and these filters keep balance in the noise elimination and the fringe details preservation, especially with abrupt fringe change, e.g., the edge of urban structures. However, tensor decomposition based on batch processing cannot deal with few newly acquired interferograms filtering directly. The filtering of dynamic InSAR tensor is the inevitable challenge when processing InSAR stack data, where dynamic InSAR tensor denotes the size of InSAR tensor increases continuously due to the acquisition of new interferograms. Therefore, based on the online CANDECAMP/PARAFAC (CP) decomposition, we propose an online filter to fuse data and process the dynamic InSAR tensor, named OLCP-InSAR, which performs well especially for the urban area. In this method, CP rank is utilized to measure the tensor sparsity, which can maintain the structural features of the InSAR tensor. Additionally, CP rank estimation is applied as an important step to improve the robustness of Online CP decomposition - InSAR(OLCP-InSAR). Importing CP rank and outlier’s position as prior information, the filter fuses the noisy interferograms and decomposes the InSAR tensor to acquire the low rank information, i.e., filtered result. Moreover, this method can not only operate on tensor model, but also efficiently filter the new acquired interferogram as matrix model with the assistance of chosen low rank information. Compared with other tensor-based filters, e.g., high order robust principal component analysis (HoRPCA) and Kronecker-basis-representation multi-pass SAR interferometry (KBR-InSAR), and the widespread traditional filters operating on a single interferometric pair, e.g., Goldstein, non-local synthetic aperture radar (NL-SAR), non-local InSAR (NL-InSAR), and InSAR nonlocal block-matching 3-D (InSAR-BM3D), the effectiveness and robustness of OLCP-InSAR are proved in simulated and real InSAR stack data. Especially, OLCP-InSAR can maintain the fringe details at the regular building top with high noise intensity and high outlier ratio.

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.