Phase decorrelation hampers the accuracy of distributed scatterer (DS) 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 ministacks based on the coherence pattern, rather than constant-size ministacks 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 (LR), 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.

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 covariance 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 introducingL1-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 ofL2-norm regularization. Both synthetic data tests and real Sentinel-1 data covering Changi Airport, Singapore, demonstrate the validity of the proposed approach.

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 minimumL1-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.

Tropospheric delays (TDs) still hinder the millimeter-scale measurement accuracy of interferometric synthetic aperture radar (InSAR). Towards the higher accuracy, this letter presents a new time series TDs correction method. The rationale behind the proposed method is that multi-view clustering (MvC) is introduced to identify the spatiotemporal TDs behaviors, particularly, in which one-pass multi-view clustering (OPMC) algorithm is employed to perform window segmentation rather than sticking to the commonly used boxcar windows. Next, a phase-elevation network correction model in each cluster is constructed by fully considering the spatiotemporal phase information. Besides, an iterative weighted scheme is designed to further enhance the robustness of the estimated model parameters. The Sentinel-1 datasets covering the southwest mountainous area, China, confirm the effectiveness of the new method.

As a supplement to time-series interferometric synthetic aperture radar (TS-InSAR), time-series multiple-aperture InSAR (TS-MAI) can measure the spatiotemporal changes in SAR along-track surface deformation. TS-MAI is often applied with low-frequency SAR data (e.g., L-band data) due to its ability to retain high interferometric coherence. However, the low-frequency SAR signal is vulnerable to ionospheric delays, which can significantly degrade the measurement accuracy of TS-MAI. This letter presents an approach to correct the ionospheric errors in TS-MAI. A polynomial cubic model is employed to constrain the ground deformation, which is then incorporated into the observation model for effectively separating the deformation signal and the ionospheric delays. The proposed method is tested using the L-band ALOS-1 PALSAR-1 datasets covering the Tocopilla area in Chile between November 2007 and March 2011. The correction performance and accuracy of the proposed method are demonstrated by comparing the range split-spectrum interferometry (RSSI)-based method and the local GPS data, respectively. The root mean square error (RMSE) improvement rates between TS-MAI and GPS are 72.17% for the SRGD site and 84.51% for the VLZL site, and their correlation coefficients increase from 0.23 and 0.50 to 0.52 and 0.61 after the correction.

Ionospheric phase delay is a critical error source in Time Series Interferometric Synthetic Aperture Radar (TS-InSAR) for the purpose of monitoring ground surface deformation with SAR data obtained from low-frequency radar systems. Recently, the Range Split-Spectrum Interferometry (RSSI) method has been employed to estimate and rectify ionospheric errors in TS-InSAR. However, the performance of the RSSI method is largely restricted by the significant linear scale factors resulting from the current small SAR bandwidth. In this study, we propose a Reformulating RSSI (Re-RSSI)-based method for correcting the ionospheric error in TS-InSAR by optimizing the linear scale factors, with the aim of improving the accuracy of TS-InSAR measurements. We evaluate the Re-RSSI method using 121 ALOS-1 PALSAR images that cover two distinct regions: the low-latitude Lazufre volcano region and the high-latitude Anaktuvuk River tundra fire region. Our results demonstrate that the Re-RSSI method can effectively remove time series ionospheric errors at both test sites, where we detected ionospheric delays of approximately 2.5 cm/yr and 2.0 cm/yr, respectively. Using Global Navigation Satellite System (GNSS) measurements as ground truth, we achieved an 86.59% improvement rate in root mean square error (RMSE) with the Re-RSSI method, which is significantly higher than the 66.40% improvement rate achieved with the traditional RSSI method.

The new generation of SAR satellites is serving our long-standing demand for high-resolution crustal deformation over various scales. However, the reliability of InSAR measurements is still limited by varying tropospheric conditions between acquisitions, especially when mapping slow-deforming interseismic deformation. We propose here a new phase-based approach for mapping interseismic deformation using short-period interferograms. Our method formulates the InSAR phase after topographic correction as the sum of three components: (1) spatiotemporally varied turbulent tropospheric phase, (2) topography-correlated stratified tropospheric phase, and (3) interseismic-related deformation assumed to be accumulated at a constant rate. We simultaneously solve for the parameters in the model to avoid overestimating the tropospheric phases, especially when interseismic deformation and tropospheric delays are both coupled with elevation in space. Synthetic tests and practical applications to easternmost Altyn Tagh fault demonstrate that the new method can effectively recover the small-amplitude interseismic deformation caused by fault motion even when the interferograms are dominated by strong tropospheric delays.

Orbital error, one of major error sources of InSAR observations, is characterized by long wavelength artifacts which can downgrade the monitoring accuracy, especially for wideswath SAR missions. In this paper, 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 integratesL2-Norm withL1-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 through building up 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.

With the increasing amount of synthetic aperture radar (SAR) data with various imaging geometries (at least ascending/descending tracks), it is possible to obtain accurate multi-dimensional (MD) deformation time series with long time span. However, in most cases SAR data of different geometries are un-synchronously acquired over the same region, making it impossible to directly solve the underdetermined observation model (OSM) between the interferometric SAR (InSAR) measurements and the MD deformations. Kalman filter (KF), as one of the most famous dynamic estimators, can obtaina prioriinformation of the unknowns based on the preexisting time series, therefore it can be used to deal with this InSAR underdetermined problem. This article employs the KF to realize the dynamic estimation of MD deformations with short-baseline interferograms. The innovation lies in the establishment of the KF state transition model (STM) and OSM, which aims to make the InSAR monitoring problem better adapt to the KF. Particularly, by assuming a smooth deforming process, existing deformation time series are used to establish the STM and to predict the deformations at current moment. Besides, a strain model (SM) is employed to assist the establishment of the OSM. Simulation and real experiments in the Geysers geothermal field (GGF), U.S. demonstrate that, compared with the state-of-the-art methods, the proposed KF method allows more robust deformation estimation and achieves higher computational efficiency for dynamic estimation.

Time Series SAR interferometry (InSAR) (TS-InSAR) has been widely applied to monitor the crustal deformation with centimeter- to millimeter-level accuracy. Phase unwrapping (PU) errors have proven to be one of the main sources of bias that hinder achieving such high accuracy. In this article, a new time series PU approach is developed to improve the unwrapping accuracy. The rationale behind the proposed method is to first improve the sparse unwrapping by mitigating the phase gradients in a 2-D network and then correcting the unwrapping errors in time, based on the triplet phase closure. Rather than the commonly used Delaunay network, we employ the all-pairs-shortest-path (APSP) algorithm from graph theory to maximize the temporal coherence of all edges and to approach the phase continuity assumption in the 2-D spatial domain. Next, we formulate the PU error correction in the 1-D temporal domain as compressed sensing (CS) problem, according to the sparsity of the remaining phase ambiguity cycles. We finally estimate phase ambiguity cycles by means of integer linear programming (ILP). The comprehensive comparisons using synthetic and real Sentinel-1 data covering Lost Hills, California, confirm the validity of the proposed 2-D + 1-D unwrapping approach and its superior performance compared to previous methods.

Time-series SAR interferometry (TS-InSAR) has been widely used to map the millimeter-scale interseismic displacements. Tropospheric noise is still a key error source that hinders further improvement of such measurement. In this article, a new spatiotemporal TS-InSAR tropospheric noise filtering is proposed to approach higher accuracy measurements. We first construct a 2-D arc network for all the data points, and based on that a temporal high-pass and spatial low-pass filtering is applied to estimate the tropospheric noise for all the points. To better filter out long-wavelength interseismic displacements in temporal high-pass filtering, we construct four-candidate time-series models to model the displacement histories for each arc. To avoid overfitting, the F hypothesis test is applied to select the most suitable model for all arcs. Notably, instead of the commonly used Delaunay network, the all-pairs-shortest-path algorithm in the graph theory is employed to reconstruct all arcs and to improve the applicability of the time-series model. Comprehensive tests using synthetic data and Sentinel-1 data covering Central San Andreas Fault (CSAF) creep section validate our tropospheric noise removal approach in measuring the interseismic velocity across the fault.

How to obtain millimeter-scale along-track deformations using phase measurements is still a pending question for InSAR community. Although Burst Overlap Interferometry (BOI) technique makes this question seem tractable, most applications of BOI still focus on extracting centimeter-scale deformations for co-seismic cases. To further improve measurement accuracy, here we propose a new time series BOI algorithm towards maximizing the performance of BOI and obtaining as high accuracy of the along-track deformations as possible. This algorithm has three major steps. The first step is to enhance BOI phase signal-to-noise ratio using our newly proposed phase estimator. In the second step, we apply a strain model-based method to further suppress the phase noise and rescue more data points. In the third step, a misregistration correction procedure which considers plate motion is applied to mitigate BOI time series bias. We tested our proposed algorithm over the Chaman fault. Although the derived millimeter-scale deformations demonstrate the effectiveness of our method, experimental results show that decorrelation and ionospheric disturbance are still two great challenges of BOI techniques.

In the coming era of synthetic aperture radar (SAR) big data, the in-orbit Sentinel-1 mission will provide unprecedented data with an increasing volume. As a fundamental step of time-series analysis for such large and growing amount data, terrain observation by progressive scans (TOPS) co-registration still presents a relative challenge: 1) low coherence scenarios may degrade the estimate accuracy and 2) unprecedented and growing data volume increases the computational burden. To overcome both limitations, this article presents a sequential approach for TOPS time-series co-registration, with an emphasis on the enhanced spectral diversity (ESD) estimate accuracy over low coherence scenes. We first employ double sample over the burst overlap region to improve the statistical proprieties of sample covariance matrix, followed by ESD phase estimation using a phase linking algorithm. Then, we carry out the sequential co-registration on each mini-stack without the necessity for reprocessing the entire stack by introducing a data compression technique. Using synthetic data and real Sentinel-1 TOPS data over densely vegetated areas in the Yunan-Kweichow plateau, we fully evaluate the performance of presented approach and compare the results with those obtained from the state-of-the-art techniques. We found that the sequential approach can provide better time-series co-registration accuracy over low coherence scenes with the moderate computational efficiency.