Distributed scatterer interferometric synthetic aperture radar (DS InSAR) is a widely used technique for monitoring surface deformation, but its effectiveness is often compromised by temporal and spatial decorrelation, leading to degraded interferometric phase quality. Enhancing phase quality through phase linking (PL) is essential. However, existing PL methods struggle to produce high-quality sample coherence matrices (SCMs) due to the inhomogeneity and limited availability of low-coherence homogeneous samples. Consequently, accurately deriving phase matrices, sample coherence magnitude matrices (SCMMs), and precision matrices becomes challenging, significantly impacting the accuracy of PL estimation. To address these limitations, a two-step optimization-based PL (TSO-PL) method is proposed. TSO-PL integrates both the complex and real domain characteristics of the SCM and features two key innovations: 1) feature compression of the SCM (FC-SCM) to improve the signal-to-noise ratio of the phase and the accuracy of the coherence value in SCM and 2) adaptive nonlinear shrinkage of the SCMM (ANS-SCMM) to yield a more accurate SCMM by improving its structure. The simulation results demonstrate that TSO-PL is robust to variations in the estimation window size and homogeneous sample number, outperforming the phase triangulation algorithm (PTA), eigenvalue decomposition (EVD), and eigendecomposition-based maximum likelihood (EMI) methods in terms of accuracy and noise reduction. In a case study, TSO-PL improved the maximum deformation rate detection by 29.5%, 36.7%, and 31.1% compared with PTA, EVD, and EMI, respectively, with a significantly lower root mean square error (RMSE) of 11.3 mm. These findings demonstrate that TSO-PL effectively reduces phase noise, preserves fringe integrity, and enhances the identification of high-density monitoring points, leading to more accurate surface deformation assessments.

Underground mining activities often lead to large local surface displacements. In this case, the interferometric fringes are dense, the deformation gradient between adjacent pixels tends to exceed$\pi $, and traditional phase unwrapping (PU) methods that satisfy the phase continuity assumption have difficulty correctly retrieving the deformation. Deep learning-based PU methods can overcome the phase continuity assumption to a certain extent. However, deep learning-based PU methods also have shortcomings, such as weak generalization, difficulty in transfer, and lack of interpretability. To address these issues, this article presents a new PU method for large gradient deformation of mining areas that couples knowledge and a deep learning network (KLC-Net). This method integrates the knowledge of the mining area subsidence mechanism and the interferometric synthetic aperture radar (InSAR) phase prior knowledge into the learning network and constructs a knowledge-learning coupling framework of input sample constraints, objective function constraints, and network structure constraints. The simulation experiments show that when the noise level (NL) is less than$\pi $, the KLC-Net algorithm is suitable for interferograms with different imaging geometries. The actual engineering experimental results show that even under severe temporal decorrelation conditions, the KLC-Net algorithm can still effectively retrieve surface deformations up to 1.6 m with an average root mean square error (RMSE) of 23.5 mm. These experimental results show that the KLC-Net algorithm can effectively improves the ability and accuracy of PU under large gradient deformations in coal mining areas, and also improves the generalization performance and interpretability of deep learning-based PU methods.

There has been growing interest in developing more effective learning machines for tensor classification. At present, most of the existing learning machines, such as support tensor machine (STM), involve nonconvex optimization problems and need to resort to iterative techniques. Obviously, it is very time-consuming and may suffer from local minima. In order to overcome these two shortcomings, in this paper, we present a novel linear support higher-order tensor machine (SHTM) which integrates the merits of linear C-support vector machine (C-SVM) and tensor rank-one decomposition. Theoretically, SHTM is an extension of the linear C-SVM to tensor patterns. When the input patterns are vectors, SHTM degenerates into the standard C-SVM. A set of experiments is conducted on nine second-order face recognition datasets and three third-order gait recognition datasets to illustrate the performance of the proposed SHTM. The statistic test shows that compared with STM and C-SVM with the RBF kernel, SHTM provides significant performance gain in terms of test accuracy and training speed, especially in the case of higher-order tensors.