Monitoring deformation in rapidly subsiding funnels within mining areas remains a major challenge in the InSAR community. Most existing studies have primarily focused on the identification, filtering, and unwrapping of such subsidence funnels, while overlooking the issue of coherence underestimation in regions of rapid subsidence. This neglect often results in a sparse distribution of measurement points and difficulties in satisfying the continuity assumptions required for reliable phase unwrapping. To address this, this article presents a coherence-maximization algorithm to compensate for the underestimation bias caused by nonlinear phase gradients contributed from rapid subsidence in mining funnels. The algorithm begins with automatic detection of small objects by integrating the YOLOv11 model with the Slicing Aided Hyper Inference (SAHI) framework. Subsequently, each detected subsidence funnel is individually modeled from the wrapped interferometric phases using a two-dimensional mixed Gaussian model, optimized by a hybrid Simulated Annealing-Genetic Algorithm. The objective function is designed to maximize the interferometric coherence. Using both semi-simulated and real data from Sentinel-1 and LuTan-1 over Shanxi Province, China, we validated the effectiveness of the coherence-maximization algorithm under varying levels of decorrelation. The observed improvements in phase unwrapping further confirm the potential value of the proposed method for enhancing the reliability of InSAR measurements over mining-affected scenarios.

Pixel similarity measurement is a critical step in distributed scatterer (DS) interferometry, directly affecting DS phase estimation. Despite considerable efforts to improve its accuracy, existing methods still suffer from unsatisfactory performance, especially with small stack sizes. In recent years, deep neural networks have achieved remarkable breakthroughs in interferometric synthetic aperture radar (InSAR) processing. However, their potential for measuring pixel similarity in multitemporal InSAR remains unexplored. This article proposes a neural network-driven pixel similarity measurement approach, termed PSMNet. To address the challenge of accurately defining true data, a supervised learning strategy is designed. The proposed network consists of two main modules: 1) a feature extraction module that generates high-level feature images with enhanced representation and reduced noise and 2) a similarity measurement module that evaluates pixel similarity without relying on assumptions about data distribution. The network is trained on synthetic data, enabling it to generalize for different stack sizes and target characteristics. Extensive experiments on simulated and real TanDEM-X images demonstrate a significant accuracy improvement of the proposed approach, highlighting its robust performance for varying stack sizes and computational efficiency advantage compared to traditional methods. The proposed approach further enhances DS phase estimation and increases the number of measurement points, showing great promise for ground surface deformation monitoring.

Attributed network embedding seeks to depict each network node via a compact, low-dimensional vector while effectively preserving the similarity between node pairs, which lays a strong foundation for a great many high-level network mining tasks. With the advent of the era of Big Data, the number of nodes and edges has reached billions in many real-world networks, which poses great computational and storage challenges to the existing methods. Although some algorithms have been developed to handle billion-scale networks, they often undergo accuracy degradation or tempo-spatial inefficiency owing to attribute information loss or substantial parameter learning. To this end, we propose a simple, time- and space-efficient billion-scale attributed network embedding algorithm called SketchBANE in this paper, which strikes an excellent balance between accuracy and efficiency by adopting sparse random projection with 1-bit quantization to sketch the iterative closed neighborhood and maintain the similarity among high-order nodes in a non-learning manner. The extensive experimental results indicate that our proposed SketchBANE algorithm competes favorably with the state-of-the-art approaches, while remarkably reducing runtime and space consumption. Also, the proposed SketchBANE algorithm exhibits good scalability and parallelization.

The lack of attention to frequent or illegal mining activities that cause localized rapid surface subsidence can lead to significant accidents. Therefore, it is of great significance to identify and monitor such activities. The dense fringes generated by deformation gradients can affect the effectiveness and accuracy of InSAR processing. We proposed a new processing method that utilizes a two-dimensional mixed Gaussian model and mining area models to generate simulated interferograms to expand the dataset. Then we use YOLOv8 automatically detect suspected mining deformation areas from large-scale interferograms. Finally, by combining optimization algorithms with mining deformation models, we invert and model the deformation phase of the mining area, obtaining the modeled mining deformation phase results. This method can successfully detect the deformation areas and recover the deformation fringes, providing a foundation for improving the accuracy of subsequent InSAR processing.

The high-frequency gravity forward modeling relying on the residual terrain modeling (RTM) technique is essential for gravity data processing, fine gravity field modeling, geophysical inversion, and so on. However, classical gravity forward modeling methods face challenges such as series divergence and inefficient computation. To improve the computation efficiency, a novel approach using fully connected deep neural network (FC-DNN) for RTM terrain gravity field modeling is introduced in this study. By employing mean squared error (MSE) as the loss function, the method directly learns the mapping between terrain and gravity anomaly to predict RTM terrain gravity anomaly at any elevation, significantly enhancing computational efficiency. In addition, to boost the network’s generalization capability, a novel terrain information fusion regularization method is utilized to create an Improved FC-DNN with a refined loss function. The accuracy, computational efficiency, and generalization performance of FC-DNN and Improved FC-DNN are evaluated and compared in the Wudalianchi volcanic region and the Himalayas. The findings reveal that determined RTM terrain gravity fields based on both FC-DNN and Improved FC-DNN meet the mGal-level accuracy in these regions, with a remarkable 10$000\times $increase in computational efficiency compared to the classical Newtonian integration method. The Improved FC-DNN exhibits superior generalization ability, with accuracy enhancements ranging from 7% to 21% compared with FC-DNN.

With the launch of a number of multipolarimetric synthetic aperture radar (SAR) satellites, many multipolarimetric phase estimation algorithms have been introduced to reduce the decorrelation of distributed scatterers. They typically perform the traditional phase estimation on complex coherence matrix. Thus, the primary focus lies in accurately estimating the complex coherence matrix to achieve precise phase estimation. In this paper, we propose a multipolarimetric phase estimation approach with improved coherence matrix estimation, termed MPPE-CME. It includes two major steps. The first step is to select the polarimetric interferometric pairs using our proposed selection algorithm, which is adaptive and without setting any empirical parameters. In the second step, based on the selected polarimetric interferograms, we develop a dominant scattering mechanism (SM) extraction algorithm to estimate the complex coherence matrix with enhanced accuracy. The simulated experiment validates the effectiveness of the proposed polarimetric interferometric pair selection and dominant SM extraction algorithms. The real data experiment conducted at the Chengdu Tianfu International Airport demonstrates that MPPE-CME outperforms other multipolarimetric phase estimation algorithms with significantly reduced reconstructed phase noise, increased measurement point density, and improved deformation accuracy.

Distributed scatterer interferometry (DSI) is a well-known technique for ground surface deformation monitoring. Central to this process, phase estimation reconstructs a consistent phase series from all interferometric combinations. In theory, the maximum likelihood estimator (MLE) is the optimum approach for phase estimation. However, in practice, its performance is often compromised. Previous studies have demonstrated that the coherence magnitude bias is a source of error. However, other sources of error in the MLE processing remain unclear. This study systematically assesses the sources of error in phase estimation and develops a hybrid approach that corrects three identified sources of error: 1) To address the error from inhomogeneous pixels, an algorithm based on the covariance matrix preestimation and general likelihood ratio test (CMGLR) is developed to select more accurate homogeneous pixels; 2) to mitigate the bias from coherence magnitude matrix, we apply the oracle approximating shrinkage (OAS) algorithm to estimate the precision matrix with higher accuracy; and 3) to tackle the noise from interferometric phase matrix, the filtering principles are defined and the covariance matrix filtering (CMF) algorithm is designed to suppress the noise. A series of simulated experiments demonstrate the effectiveness of the proposed approach. Additionally, a real TanDEM-X experiment shows that the proposed approach can reconstruct the time series phase with reduced noise. Furthermore, the estimated deformation exhibits improvement with significantly increased measurement points MPs (>2.4 times) and higher accuracy compared to the traditional method based on the Kolmogorov–Smirnov (KS) test and sample covariance matrix (SCM). Particularly, it exhibits exceptional performance in monitoring fine structures, while the traditional method usually fails with very few MPs. These results underscore the significant potential of this approach in the realm of ground surface deformation monitoring.

Ground-based interferometric radar (GBIR) is an innovative tool for monitoring land surface subsidence and urban infrastructure deformation caused by rapid urbanization. However, the interferograms of GBIR are often contaminated by severe atmospheric effects, especially in coastal areas. In this study, we use independent component analysis (ICA) to extract atmospheric effects for the interferograms of GBIR. Analysis of the performance of ICA and traditional surface fitting methods have been carried out. The results suggest that the average improved rate of ICA is 93.05%, which is 69.33% higher than that of surface fitting.

Multitemporal InSAR is a widely used geodetic technique for measuring ground deformation. However, assessing the accuracy of InSAR deformation results is challenging, especially when field measurements such as leveling are limited in coverage or unavailable. While many studies have attempted to calculate the uncertainty of deformation using a priori InSAR stochastic models to assess the deformation reliability, these models are often biased by various factors. In this letter, we propose a new method called the Sparse Parameter Model (SPM) for InSAR deformation retrieval and uncertainty assessment when instantaneous deformation is not the focus. The method estimates the sparser deformation time series and leverages redundant SAR observations for the deformation uncertainty assessment and decorrelation noise suppression. The proposed model is tested by both simulated and real Sentinel-1 datasets and the derived deformation was validated with GPS measurements in the real application. The results demonstrated that the overall uncertainty of InSAR deformation, as estimated by the SPM, is 5.4 mm, falling well within the expected range of uncertainty, which highlights the effectiveness of the SPM in retrieving InSAR deformation and assessing uncertainty.

The maximum detectable deformation gradients (MDDG) for interferometric synthetic aperture radar (InSAR) technology is important for the selection of SAR images and processing algorithms to perform accurate slope displacement monitoring, which is strongly influenced by terrain factors in mountainous areas. In this paper, a functional model is proposed to determine the MDDG of InSAR with respect to arbitrary slope gradients/aspects and wavelengths. Based on this model, regional MDDG characteristics are explored and compared in Mao County, Sichuan Province, China. The MDDG distribution regarding on Sentinel-1, ALOS-2/PALSAR-2 and TerraSAR-X SAR satellite data using arbitrary slope gradient/aspect are derived. Furthermore, the MDDG from variable satellites for three different bands (X/C/L-band) are compared and the influence factors with respect to the wavelength and resolution on MDDG are discussed. The proposed model is helpful in selecting of SAR data or processing algorithms based on calculated MDDG, in the meanwhile, it has significant implications on the understanding and analyzing real slope displacement monitored by InSAR regarding on different SAR images in mountainous areas.

Nowadays, SAR instruments such as ESA’s Sentinel-1 constellation, ICEYE’s constellation of small and agile radar satellites, and the upcoming ALOS-4 and NASA/ISRO SAR missions provide new opportunities for near-real-time monitoring of geohazards with enhanced spatiotemporal resolution. Sequential dynamic adjustment model is regarded as an effective way to rapidly update time-series InSAR measurements. However, the accuracy of geophysical parameters of interest estimated from the conventional sequential least squares is greatly sensitive to the anomalous observations and/or anomalous prior parameter information. This letter aims to introduce the robust sequential adjustment method based on the M-estimation principle into near-real-time InSAR deformation monitoring to mitigate the effect of anomalous errors. Using both synthetic and real Sentinel-1 SAR datasets over Echigo plain in Japan, we fully evaluate the performance of the robust sequential estimation approach with respect to unwrapping errors in the SAR data stack. Measurements at 9 GPS stations located in the study area are used to validate the results. We find that the averaged RMSE of robust sequential adjustment is reduced by 15% in comparison with that of the conventional sequential least-squares method.

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.

The proper use of distributed scatterer (DS) can improve both the density and quality of synthetic aperture radar (SAR) interferometry (InSAR) measurements. A critical step in DS interferometry (DSI) is the restoration of a consistent phase series from SAR interferogram stacks. Most state-of-the-art algorithms adopt an approximate likelihood function to calculate the likelihood by replacing the true coherence matrix with its estimation, more specifically, the sample coherence matrix (SCM). However, this approximation has a drawback in that the coherence estimates are greatly biased when the coherence is low. In this study, we derive a new likelihood function without such an approximation. Accordingly, a DSI framework using this function for phase estimation and point selection is provided. In this framework, the new likelihood function serves as a cost function for phase estimation and a quality measure for DS selection. Its performance is investigated by experiments in a simulation study and a real-world case study using Sentinel-1 data over Shenzhen airport in China. The results reveal that the proposed DSI framework outperforms the existing state-of-the-art approaches in different scenarios, in terms of providing a more accurate estimation and improving DS density and coverage.

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.

The state-of-the-art techniques have demonstrated that coherence error degrades the performance of synthetic aperture radar (SAR) interferometry (InSAR) for distributed scatterers (DSs). This article aims at fully evaluating the influence of coherence error on DS InSAR time-series analysis. In particular, we present a methodology to increase the estimation accuracy of DS interferometry, with emphasis on spatiotemporal coherence refinement. The motive behind this is that bias removal and variance mitigation of sample coherence matrix impose optimum weighting for estimating phase series and geophysical parameters of interest, whereas maximization of temporal coherence in a reference network can avoid spatial error propagation during the least-squares adjustment. Rather than developing independent processing chains, we integrate this method into SqueeSAR technique and simultaneously take the advantage of StaMPS into consideration. Using simulation and real data over southwestern China, comprehensive comparisons before and after spatiotemporal coherence refinement are performed over various coherence scenarios. The results tested from different phase and displacement rate estimators validate the effectiveness of the presented method.

Automatic road extraction from synthetic aperture radar (SAR) imagery has been studied with success in the past two decades. However, a method that combines full interferometric SAR (InSAR) information is as yet missing. In this paper, we present an algorithm toward robust road extraction by fully exploring the multitemporal InSAR covariance matrix. To improve the detection performance and reduce false alarm ratio, intensity and coherence are first accurately estimated without loss of image resolution by homogeneous pixel selection and robust estimators. After the identification of road candidates from each quantity using multiscale line detectors, novel information fusion rules are applied to integrate the extracted results and generate the final road network. The method is tested and quantitatively evaluated on TerraSAR-X data sets depicting two scenes where complex road features make it hard for standard SAR-based methods. The experimental results show that the new method can achieve satisfactory detection performances.

Ground based interferometric radar (GBIR) is a revolutionary advanced measurement technique for geoscience and engineering geodesy. It is powerful for temporally and spatially dense measurements of highly dynamic target with sub-millimetric accuracy, especially in man-made structures, e.g. buildings, towers, dams and bridges. In this case study, we use a real aperture radar system, the Gamma Portable Radar Interferometer (GPRI-II), to perform near-real-time deformation monitoring of the deck (back side) of a cable-stayed bridge. As a test site, the Ting Kau Bridge at Tsuen Wan, Hong Kong, was continuously measured from two modes of observation, rotated azimuth scanning (RAS) and fixed azimuth scanning (FAS). The results reveal the wind-driven and vehicle-driven non-uniform oscillation of the bridge. The presented works demonstrate the ability of GPRI-II in bridge deformation or oscillation monitoring, which provide a new way for structural health monitoring of bridge.

Multitemporal interferometric synthetic aperture radar (InSAR) is increasingly being used for Earth observations. Inaccurate estimation of the covariance matrix is considered to be the most important source of error in such applications. Previous studies, namely, DeSpecKS and its variants, have demonstrated their advantages in improving the estimation accuracy for distributed targets by means of statistically homogeneous pixels (SHPs). However, these methods may be unreliable for small sample sizes and sensitive to data stacks showing large time spacing due to the variability of the temporal sample. Moreover, these methods are computationally intensive. In this paper, a new algorithm named fast SHP selection (FaSHPS) is proposed to solve both problems. FaSHPS explores the confidence interval for each pixel by invoking the central limit theorem and then selects SHPs using this interval. Based on identified SHPs, two estimators with respect to the despeckling and the bias mitigation of the sample coherence are proposed to refine the elements of the InSAR covariance matrix. A series of qualitative and quantitative evaluations are presented to demonstrate the effectiveness of our method.

Downsampling is a routine step before applying interferometric synthetic aperture radar (InSAR) data to earthquake inversion because of the high computational burden. In this letter, we make use of the matrix perturbation theory to describe the downsampling process, which is considered as matrix perturbation on inversion equation. First, we derive a formula to quantitatively assess the perturbation on the inversion solution caused by data downsampling. Next, we propose an equation-based InSAR data downsampling algorithm to better reduce the perturbation. The experiment with simulated data demonstrates that our new algorithm preserves the most details from full data inversion comparing with previous algorithms. Finally, we use our method to study the slip distribution of the 2008 Mw 6.3 Dangxiong earthquake.

In standard differential synthetic aperture radar interferometry, there could still be a residual tilt (orbital error) in the interferometric phase due to inaccurate baseline estimation. We demonstrated theoretically that the orbital errors were partially elevation dependent. On the basis of this, we introduced an elevation-dependent item to the conventional polynomial model to simulate, and therefore, compensate the orbital errors, as well as the small scale topographic and/or topography-related phase errors. Robust regression approach was suggested to determine the parameters of the proposed model. The model was validated with both synthetic and real ALOS PALSAR data of the Zhouqu, China mudslide. The synthetic test indicated that upon applying the refined model, the accuracies of phase measurements were improved by nearly two times, compared to those using conventional linear and quadratic models. The real data experiment indicated that after utilizing the refined model, the correlation between the interferogram and the digital elevation model of Zhouqu reduced to about 1/5 of those using linear and quadratic models. This demonstrates that the elevation-dependent phase components have been largely removed by the new model. More importantly, the interferogram corrected by the new model visibly disclosed the deformation area affected by the Zhouqu mudslide.

The coherence of radar echoes is a fundamental observable in interferometric synthetic aperture radar (InSAR) measurements. It provides a quantitative measure of the scattering properties of imaged surfaces and therefore is widely applied to study the physical processes of the Earth. However, unfortunately, the estimated coherence values are often biased due to various reasons such as radar signal nonstationarity and the bias in the estimators used. In this paper, we focus on multitemporal InSAR coherence estimation and present a hybrid approach that mitigates effectively the errors in the estimation. The proposed approach is almost completely self-adaptive and workable for both Gaussian and non-Gaussian SAR scenes. Moreover, the bias of the sample coherence can be mitigated with even only several samples included for a given pixel. Therefore, it is a more pragmatic method for accurate coherence estimation and can be applied actually. Different data sets are used to test the proposed method and demonstrate its advantages.

A novel coherence estimation method for small data sets is presented for interferometric synthetic aperture radar (SAR) (InSAR) data processing and geoscience applications. The method selects homogeneous pixels in both the spatial and temporal spaces by means of local and nonlocal adaptive techniques. Reliable coherence estimation is carried out by using such pixels and by correcting the bias in the estimated coherence caused by the non-Gaussianity in high-resolution SAR scenes. As an example, the proposed method together with coherence decomposition is applied to extract the temporal decorrelation component over an area in Macao. The results show that the proposed algorithms work well over various types of land cover. Moreover, the coherence change with time can be more accurately detected compared to other conventional methods.

We map the coseismic deformation of the 2011 Tohoku-Oki earthquake with data from three descending Envisat/ASAR tracks and six ascending ALOS/PALSAR tracks that cover most of northeastern Japan. Due to the inaccurate estimation of the satellite status, orbital ramps commonly exist in the coseismic interferograms, which resulted in inconsistency among the deformation maps released by several research groups. In this letter, calibration has been performed to accurately remove these ramps by a 2-D quadratic-phase model derived based on GPS measurements from the ARIA team at the Jet Propulsion Laboratory and Caltech. The average RMS of the interferometric synthetic aperture radar (InSAR) measurements, as compared with GPS measurements at the validation stations, has decreased from 17.8 to 7.7 cm after the orbital ramp correction is made, indicating that much more accurate InSAR measurements are achieved. The corrected coseismic deformation from the InSAR measurements is consistent with not only the GPS observations at the individual GPS stations but also with the coseismic deformation interferogram from interpolated GPS observation in the SAR viewing directions. The corrected coseismic deformation measurement results show a maximum line-of-sight displacement of up to 3.7 m from the ascending PALSAR tracks and 2.4 m from the descending ASAR tracks, respectively.