In this paper, we address some questions with respect to the Tianshan Mountains that are necessary for understanding the present deformation rate in this region. A series of thrust nappe structures are distributed on the north and south sides of the Tianshan Mountains, and many of them are currently active. To analyze the deformation characteristics and movement rates of different fold-and-thrust belts on the northern and southern margins of Tianshan, we use InSAR observations (Sentinel-1A/B, 2015–2020) to produce a rate map for the entire observation period on four ascending and four descending tracks. In order to reduce phase artifacts, we reconstruct multi-temporal scenes with atmospheric-corrected and orbital-corrected interferograms via a small baseline subset. The results show that the Bolokenu-Aqikekuduke Fault exhibits a right-lateral strike-slip motion, with the western segment moving at about 4.95 ± 0.38 mm/yr and the eastern segment at approximately 2.34 ± 0.34 mm/yr. The Manas-Tugulu anticline in the northern fold-and-thrust belt reaches ~5–8 mm/yr at 86°E–86.5°, and the Qiulitage anticline in the south reaches ~6–9 mm/yr at ~83°–85°. The post-seismic time series cumulative displacement map of the Jinghe earthquake reveals no significant post-seismic deformation signal in the epicenter area. The Qiulitage thrust belt, situated within the fold-and-thrust belts flanking the Tianshan, features extensive thrust accompanied by a right-lateral strike-slip component. And the Manas-Tugulu anticline exhibits sustained deformation, including pronounced coseismic and post-seismic effects from the Hutubi earthquake. This study highlights the potential of a multi-temporal InSAR analysis and emphasizes future opportunities presented by new generations of SAR platforms with shorter revisit periods for quantifying the spatial and temporal behavior of post-seismic and interseismic periods.

How to improve the phase signal-to-noise ratio (SNR) of distributed scatterers (DSs) is a key topic in DS interferometry (DSI). Although some state-of-the-art phase linking (PL) estimators have been proposed, their performance is still limited by the accuracy of the estimated sample coherence matrix (SCM). The key challenges arise from the biased estimation of the near-zero coherence matrix (the magnitude matrix of SCM) under conditions of small sample sizes and heterogeneous samples. To overcome this limitation, we present a sparse regularization-based PL estimator that considers the potential sparsity structure of the inverse covariance matrix. In this new estimator, we first introduced the graphical lasso (GLasso) algorithm into the small samples estimation problem of SCM, which suppresses the biased estimation of the sparse inverse covariance matrix by introducing ${L}_{{1}}$ -norm regularization, significantly reducing the impact of weakly coherent interferograms in fast decorrelation scenarios. Furthermore, we also attempt to generalize this scheme to long-term coherence cases through the utilization of ${L}_{{2}}$ -norm regularization. Both synthetic data tests and real Sentinel-1 data covering Changi Airport, Singapore, demonstrate the validity of the proposed approach.

Decorrelation is a major obstacle to the application of multitemporal interferometric synthetic aperture radar (InSAR) in areas with low coherence. Distributed scatterers (DSs) with similar backscattering in the spatial neighborhood are the key to improving the observational density and accuracy of deformation estimation in fast decorrelation regions. Phase series estimation from all possible interferograms is expected to improve the signal-to-noise ratio (SNR) and further enhance the sensitivity of deformation measurement. The coherence bias and the efficiency of the phase estimation raise concerns. In this article, we propose a computationally attractive algorithm for the interferometric phase estimation, namely alternating projection (AP), which is a combination of the alternating maximization and the projection matrix decomposition methods. The homogenous pixel selection and coherence estimation bias correction are conducted by the FaSHPS algorithm and DSIpro software toolbox. Results of simulations and real SAR data show that the proposed AP method could reconstruct credible phase series comparable to the quasi-Newton optimization algorithm [Broyden–Fletcher–Goldfarb–Shanno (BFGS)] while having three times the efficiency gain.

Phase Unwrapping (PU) based on spatial networks is a key procedure in time series synthetic aperture radar interferometry (TS-InSAR). Although the state-of-the-art techniques have shown good success in common cases, their performance remained uncertain in some challenging cases where the reliability of spatial network is difficult, e.g., reservoir areas with sparse points. In this context, this letter presents a new 3D PU method based on the fully connected spatiotemporal network (FCSN) to improve both accuracy and robustness of PU. The rationale behind is that we first implement a spatiotemporal network refinement including temporal interferogram pair selection and spatial network optimization. Based on the generated spatiotemporal network, we then establish a 3D PU mathematical framework by elaborating the 2D edgelist PU theory into the 3D domain. In this framework, all interferograms are unwrapped using integer linear programming method under the minimum L ¹ -Norm criterion. The new feature of the proposed method is that after a single solution search, all interferograms are unwrapped with a relatively high accuracy. The experimental results on two real datasets confirm its effectiveness.

Phase decorrelation hampers the accuracy of distributed scatterer interferometry (DSI) in high-precision deformation monitoring. While several advanced phase linking (PL) techniques built upon the sample coherence matrix (SCM) have shown effectiveness in enhancing the signal-to-noise ratio (SNR), their performance significantly degrades under suboptimal SCM estimation, particularly in scenarios of fast decorrelation and near-zero coherence levels. This article presents an enhanced sequential phase estimator motivated by the degradation of theoretical accuracy due to pure noise-bearing interferograms in full-stack-exploiting PL schemes. In the proposed estimator, Bayesian ensemble theory is first employed to divide the full-stack data adaptively into mini-stacks based on the coherence pattern, rather than constant-size mini-stacks usually determined empirically. Building on this, the estimator introduces a nonconvex regularization-based sparse SCM by constraining the coherence matrix to have potential sparsity and low-rank, which suppresses the influence of noisy interferometric pairs and improves SCM estimation. Moreover, we incorporate the deformation elasticity theory to provide additional spatial constraints on the reconstructed phase time series across adjacent pixels, realized by using the strain model to reduce phase discontinuity and further enhance the SNR. Experiments on the simulated and real Sentinel-1 images over a landslide-prone area in western Guizhou, China, demonstrate the effectiveness and superior performance of the new method.

Orbital error, one of the major error sources of InSAR observations, is characterized by long-wavelength artifacts which can downgrade the monitoring accuracy, especially for wide-swath SAR missions. In this letter, we present a novel approach for time-series orbital error correction, with an emphasis on the computational and estimation efficiency of orbital error parameters over wide-area scale scenes. The proposed method combines the temporal triplet network and shrunken estimator, which integrates $L^{2}$ - with $L^{1}$ -Norm regularization, also known as Lasso regularization. The rationale behind it is to first determine the initial orbital parameters by utilizing the traditional polynomial-based method in the spatial domain. Next, in order to weaken the interference of phase unwrapping errors and other undesired phase contributions, an additional correction procedure is implemented by building up a redundant triplet network in the time domain and further a shrunken estimation method. Experiments on synthetic data and real Sentinel-1 datasets covering Eastern California confirm that the presented method can better balance the accuracy and computational efficiency. The proposed approach may, therefore, be useful for the processing of emerging big data InSAR.