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.

Quantifying the precision of Interferometric Synthetic Aperture Radar (InSAR) deformation monitoring is a fundamental aspect of ensuring its reliability in operational applications. Traditional uncertainty estimation methods, which are based on phase noise and error propagation laws, tend to overestimate monitoring precision. In this study, we systematically investigate the combined effects of coherence, deformation magnitude, SAR wavelength, and spatial resolution on monitoring uncertainty through multi-parameter-controlled experiments. Based on this, a wavelength-coherence integrated function model, referred to as the InSAR Deformation Monitoring Uncertainty model (In-DMU), was developed to estimate the precision of the deformation measurements. To rigorously define applicability of the model, a Pettitt test based on sliding window standard deviation (Pt-SWStd) is used to detect change points in the error distribution, thus establishing critical gradient thresholds of 6.433 mm/m (L-band), 1.407 mm/m (C-band), and 0.456 mm/m (X-band). Beyond these thresholds, phase unwrapping constraints lead to the retrieval breakdown regime, limiting reliable deformation estimation. Furthermore, the influence of multi-looking processing on the In-DMU model was systematically quantified. To assess practical applicability, the In-DMU model was validated across diverse observational scenarios using data from five representative SAR satellites: ALOS-1 (L-band), ALOS-2 (L-band), Radarsat-2 (C-band), Sentinel-1 (C-band), and TerraSAR-X (X-band). The In-DMU model provides a universal tool for priori estimation of InSAR monitoring precision, offering valuable guidance for SAR data selection and optimization of multi-looking configurations.

Interferometric phase optimization is a critical step in multitemporal Interferometric Synthetic Aperture Radar (MT-InSAR). The advent of multi-polarimetric SAR satellites has boosted the polarimetric interferometric phase optimization techniques, where the polarimetric information can be used to enhance the interferometric phase quality. Polarimetric interferometric phase optimization approaches mainly include polarimetric coherence optimization (PCO) and polarimetric phase linking (PPL) algorithms. PCO algorithms that with good performance like Exhaustive Search Polarimetric Optimization (ESPO) are with high computational cost, especially for quad-polarimetric data cases. PPL algorithms mainly focus on distributed scatterers (DSs) and do not adopt the adaptive optimization for PS pixels. In addition, their DSs selection merely depends on the number of statistically homogeneous pixels (SHPs) through setting a threshold whose determination approach is usually not clearly defined. Moreover, the interferometric phase estimation results of PPL are affected by heterogeneous pixels. To overcome these limitations, by employing the total power polarization optimization and non-local PL, an adaptive polarimetric interferometric phase optimization algorithm for both PS and DS pixels is developed. The proposed algorithm has been evaluated using the simulated data, quad-polarimetric UAVSAR data, and dual-polarimetric Sentinel-1 data. The results demonstrate that in comparison with the previous methods, the proposed algorithm achieves superior interferometric phase quality, along with improved effectiveness and efficiency.

Distributed scatterer (DS) is prone to be seriously disturbed in differential interferometric process due to spatiotemporal decorrelation noise. Phase linking (PL) plays a pivotal role in DS interferometry (DSI) as it facilitates the recovery of the DS phase series from the temporal interferogram stack. Currently, the existing PL algorithms mainly rely on the statistically homogeneous pixels (SHPs) within a fixed patch to construct the sample complex coherence matrix (SCM). Nevertheless, these methods suffer from issues, such as the absence of spatial constraints, insufficient utilization of possible SHPs outside the window, and vulnerability to heterogeneous samples. To overcome the aforementioned limitations, this article proposes a nonlocal phase linking (NL-PL) approach inspired by the concept of NL means. NL-PL converts the resemblance between individual pixels and their homogenous neighboring counterparts into weights, which are subsequently used to perform a weighted average of the SCM. The weighted SCM is then employed in PL to achieve the optimization estimation of DS phase. The performance of the proposed method is evaluated using simulated data as well as real Sentinel-1 satellite data. The experimental results suggest that in contrast to conventional PL techniques, the proposed NL-PL approach showcases enhanced efficacy in suppressing noise and smoothing phase. Moreover, it enables a higher posterior coherence, thereby augmenting the count of DS sampling points. Furthermore, the findings of this study prove the performance and the adaptability of NL-PL in scenarios characterized by a scarcity of homogeneous samples and an abundance of heterogeneous samples.

Accurately locating goafs is critical for identifying illegal mining, preventing mining-related geohazards, and facilitating the development and utilization of underground spaces. Conventional methods for locating goafs with InSAR techniques primarily rely on the Probability Integral Model (PIM), which tends to overestimate the ground deformation under subcritical extraction. On the other hand, the number of subcritical extraction working faces significantly rises with mining depth. Under these circumstances, accurately locating subcritical underground goafs using existing methods becomes challenging. To this end, a novel method, which incorporates the improved probability integral model (IPIM) and InSAR technique for locating subcritical goafs, is proposed, named the locating goaf method based on IPIM (LGM-IPIM). Firstly, based on the IPIM, a model between the subcritical goaf parameters and InSAR-derived deformation is built. Then, to reduce the influence of surrounding mining, the goaf azimuth angle is determined with textures and patterns of the InSAR-derived deformation time series. Finally, the genetic algorithm-particle swarm optimization (GA-PSO) is employed to determine the goafs’ parameters. The effectiveness of the proposed algorithm has been verified by simulation and real data. The results demonstrate that the proposed LGM-IPIM outperforms conventional methods, presenting the best performance and the highest accuracy. Specifically, compared to the locating goaf method based on PIM (LGM-PIM), the proposed LGM-IPIM improves the location accuracy of goaf boundary points by 28.90% and 86.23% in Areas A and B, respectively. In addition, the proposed LGM-IPIM has robustness against minor errors within the deformation monitoring and IPIM parameters.

Underground coal fires are global catastrophes that result in energy waste, carbon emission, and eco-environment pollution. Remote sensing (RS) detection is essential for underground coal fire extinguishing engineering, and the most used is thermal infrared (TIR) RS. It can well obtain the thermal anomalies of land surface temperature (LST), which is the most direct surface feature of underground coal fires. However, most studies using TIR RS simply delineate underground fire sources vertically according to LST anomalies, which has relatively little impact when initially determining coal fire area locations on the large scale. As for the precise location of small-scale subsurface fire sources, the deviation between subsurface fire source locations inferred and real locations could lead to errors or even mistakes to fire extinguishing engineering. There is a lack of subsurface fire source evolution model reconstruction method, and the spatiotemporal correlations characteristic of LST thermal anomalies and underground fire sources have not yet been discussed. To this end, taking Miquan coalfield (Western China) as an example, a 3-D empirical Bayesian Kriging (EBK3D) method is first proposed to reconstruct the 4-D temperature fields of underground fire sources. Then, the feasibility of the vertical correspondence approach to inferring small-scale subsurface fire sources through LST thermal anomalies detected by unmanned aerial vehicle TIR RS and satellite TIR RS is analyzed. Finally, the spatiotemporal correlation characteristic of LST thermal anomalies and subsurface fire sources is analyzed. As the results show, it is feasible to reconstruct the underground fire source evolution model by the EBK3D method. The reconstructed 4-D temperature fields can dynamically reflect the evolutionary states of underground fire sources in three time periods, with cross-validated root mean square errors of 52.2 °C, 49.6 °C, and 37.1 °C and$R^{2}$of linear regressions of 0.925, 0.9145, and 0.8429, respectively. The LST thermal anomalies show a significant spatiotemporal delay with respect to the subsurface fire source evolution. This makes the locations of the underground fire sources traced by the vertical correspondence method deviate from the real ones. The offsets of underground fire sources relative to surface thermal anomalies in the coal seam strike and dip directions for different time periods at depths of (T1: −44.43 m, T2: −27.72 m, and T3: −20.04 m) are (T1: 73.80 m, T2: 52.33 m, and T3: 45.06 m), and (T1: 16.79 m, T2: 17.27 m, and T3: 24.82 m), respectively.$R^{2}$’s for the linear regression model of the offset averages in three directions versus time and fire source size are (0.9247, 0.7949, and 0.9564) and (0.8739, 0.85 and 0.9152), respectively.

The use of polarimetric SAR data can improve the performance of persistent scatterer interferometry (PSI). However, its huge potential remains locked for the amplitude information based offset tracking (OT) technology. For example, to the best knowledge of the authors, there is no single example of a polarization based image optimization method that has been developed for OT processing. In this paper, an amplitude contrast enhancement algorithm (ACE) is introduced, which demonstrates the potential of the polarimetric SAR data on the improvement of OT performance. Its core idea is finding the optimal combination of the different scattering mechanisms for each pixel to improve the contrast. Firstly, the orientation of the reflected polarization ellipse is removed, to avoid the influence of the geometric relationship between the antenna and the target, and the properties of the target. Then three similarity parameters are defined to represent the three basic reflection types of the single bounce, the double bounce, and the random reflection. After that, the optimizing equation is constructed with two optimizing vectors. Finally, the optimizing vectors are calculated to obtain the enhanced amplitude image. Three examples of the enhancement are presented with different PolSAR images sets of both full- (Radarsat-2) and dual-polarization (TerraSAR-X and Sentinel-1). The performance of ACE-OT has been compared with another method, the Adaptive Histogram Enhancement (AHE). The impact of the number of polarization channels available on ACE-OT performance has also been studied.

Polarimetric persistent scatterer interferometry (PolPSI) takes advantage of polarimetric optimization algorithms that enhance interferograms’ phase quality by adequately combining the available polarization channels (e.g., HH, VV, HV, and VH) into an improved one. Amplitude dispersion ($D_{A}$) is one of the commonly used phase quality metrics for this optimization. The resolution of the images is supposed to have an impact on the performance of$D_{A}$-based PolPSI in terms of both pixel density and quality. In this research, this impact is investigated. Specifically, 30 quad-pol RADARSAT-2 images over Barcelona with a resolution around 5 m in both range and azimuth are employed to generate additional data sets with degraded resolutions, ranging from 7.5 to 20 m. The results confirm that, in all cases, the ability of$D_{A}$to select high-quality pixels, i.e., persistent scatterers, decreases when the spatial resolution worsens because the loss of resolution increases the number of scatterers present in a resolution cell. In addition, it would be expected that the performance of the polarimetric optimization of$D_{A}$would tend to decrease when the spatial resolution worsens. However, for all employed resolutions, the polarimetric optimization improves the density and quality of PSs with respect to that of any single polarimetric channel. Moreover, this improvement is more noticeable, in relative terms, as the image resolution degrades.

Polarimetric persistent scatterer interferometry (PolPSI) takes advantage of polarimetric optimization algorithms that enhance interferograms' phase quality by adequately combining the available polarization channels (e.g., HH, VV, HV and VH) into an improved one. Amplitude dispersion ($D_{A}$) is one of the commonly used phase quality metrics for this optimization. The resolution of the images is supposed to have an impact on the performance of$D_{A}$based PolPSI in terms of both pixels density and quality. In this research, this impact is investigated. The results confirm that in all cases the ability of the$D_{A}$to select high-quality pixels, i.e. Persistent Scatterers, decreases when the spatial resolution worsens because the loss of resolution increases the number of scatterers present in a resolution cell. However, for all employed resolutions (ranging from around 5 m to 20 m) the polarimetric optimization improves the density and quality of PSs with respect to that of any single polarimetric channel. Moreover, this improvement is more noticeable, in relative terms, as the image resolution degrades.

Speckle noise and decorrelation can hamper the application and interpretation of PolSAR images. In this paper, a new adaptive multitemporal Pol(DIn)SAR filtering and phase optimization algorithm is proposed to address these limitations. This algorithm first categorizes and adaptively filters permanent scatterer (PS) and distributed scatterer (DS) pixels according to their polarimetric scattering mechanisms [i.e., the scattering-mechanism-based filtering (SMF)]. Then, two different polarimetric DInSAR (POLDInSAR) phase OPTimization methods are applied separately on the filtered PS and DS pixels (i.e., POLOPT). Finally, an inclusive pixel selection approach is used to identify high-quality pixels for ground deformation estimation. Thirty-one full-polarization Radarsat-2 SAR images over Barcelona (Spain) and 31 dual-polarization TerraSAR-X images over Murcia (Spain) have been used to evaluate the performance of the proposed algorithm. The PolSAR filtering results show that the speckle of PolSAR images has been well reduced with the preservation of details by the proposed SMF. The obtained ground deformation monitoring results have shown significant improvements, about ×7.2 (the full-polarization case) and ×3.8 (the dual-polarization case) with respect to the classical full-resolution single-pol amplitude dispersion method, on the valid pixels' densities. The excellent PolSAR filtering and ground deformation monitoring results achieved by the adaptive Pol(DIn)SAR filtering and phase optimization algorithm (i.e., the SMF-POLOPT) have validated the effectiveness of this proposed scheme.

The rationale of polarimetric optimization techniques is to enhance the phase quality of the interferograms by combining adequately the different polarization channels available to produce an improved one. Different approaches have been proposed for polarimetric persistent scatterer interferometry (PolPSI). They range from the simple and computationally efficient BEST, where, for each pixel, the polarimetric channel with the best response in terms of phase quality is selected, to those with high-computational burden like the equal scattering mechanism (ESM) and the suboptimum scattering mechanism (SOM). BEST is fast and simple, but it does not fully exploit the potentials of polarimetry. On the other side, ESM explores all the space of solutions and finds the optimal one but with a very high-computational burden. A new PolPSI algorithm, named coherency matrix decomposition-based PolPSI (CMD-PolPSI), is proposed to achieve a compromise between phase optimization and computational cost. Its core idea is utilizing the polarimetric synthetic aperture radar (PolSAR) coherency matrix decomposition to determine the optimal polarization channel for each pixel. Three different PolSAR image sets of both full- (Barcelona) and dual-polarization (Murcia and Mexico City) are used to evaluate the performance of CMD-PolPSI. The results show that CMD-PolPSI presents better optimization results than the BEST method by using either $D_{\mathrm{ A}}$ or temporal mean coherence as phase quality metrics. Compared with the ESM algorithm, CMD-PolPSI is 255 times faster but its performance is not optimal. The influence of the number of available polarization channels and pixel's resolutions on the CMD-PolPSI performance is also discussed.

Pixel selection is a crucial step of all advanced Differential Interferometric Synthetic Aperture Radar (DInSAR) techniques that have a direct impact on the quality of the final DInSAR products. In this paper, a full-resolution phase quality estimator, i.e., the temporal phase coherence (TPC), is proposed for DInSAR pixel selection. The method is able to work with both distributed scatterers (DSs) and permanent scatterers (PSs). The influence of different neighboring window sizes and types of interferograms combinations [both the single-master (SM) and the multi-master (MM)] on TPC has been studied. The relationship between TPC and phase standard deviation (STD) of the selected pixels has also been derived. Together with the classical coherence and amplitude dispersion methods, the TPC pixel selection algorithm has been tested on 37 VV polarization Radarsat-2 images of Barcelona Airport. Results show the feasibility and effectiveness of TPC pixel selection algorithm. Besides obvious improvements in the number of selected pixels, the new method shows some other advantages comparing with the other classical two. The proposed pixel selection algorithm, which presents an affordable computational cost, is easy to be implemented and incorporated into any advanced DInSAR processing chain for high-quality pixels' identification.

Multilooking is an effective speckle reduction tool for InSAR images. However, it has some limitations. Based on the De-specKS and NL-SAR algorithms, an adaptive multilooking scheme for multi-temporal InSAR data has been proposed in this paper. Simulated and real SAR data sets have been employed to evaluate the performance of this scheme. The results show that, by taking advantages of DespecKS and NL-SAR, the proposed scheme presents better detail preservation and speckle noise reduction performances comparing with these two advanced and classical multilooking algorithms.