Coherence magnitude is a key metric for assessing the similarity between two synthetic aperture radar (SAR) signals, playing an essential role in high-quality interferometric SAR (InSAR) phase processing and the analysis of Earth’s surface characteristics. However, coherence estimation often suffers from upward bias due to limited independent samples, particularly in low-coherence regions. This study proposes a regularization-based approach to reduce coherence estimation bias, specifically in areas with limited homogeneous samples. By adaptively determining regularization parameters and prior coherence using nonlocal homogeneous pixel estimation, the method effectively minimizes bias while maintaining computational efficiency. Validated through Monte Carlo simulations and real data from 16 TerraSAR-X images of Shanghai, the proposed approach outperforms conventional techniques, exhibiting reduced residual bias and lower estimation standard deviation across diverse scenes.

Interferometric Synthetic Aperture Radar (InSAR) has become an essential tool for monitoring surface deformation with high precision and wide spatial coverage. Among various InSAR techniques, the Stacking InSAR approach is widely used for geological hazard assessments due to its computational efficiency and robustness against decorrelation noise. However, Digital Elevation Model (DEM) errors remain a significant challenge, introducing spurious deformation signals and degrading deformation rate estimates. We present here a rigorous analysis of the impact of DEM errors on Stacking InSAR-derived deformation rates and introduce an enhanced method that effectively mitigates these errors. Unlike conventional correction techniques that require explicit DEM error estimation, the proposed method leverages perpendicular baseline averaging, eliminating DEM-induced biases while maintaining computational simplicity. The method is validated using both simulated and real Sentinel-1A datasets from two tracks, with results compared against conventional Stacking and Small Baseline Subset (SBAS) approaches. The findings demonstrate that the proposed method significantly improves deformation rate estimation by suppressing DEM-induced artifacts, thereby enhancing the reliability of InSAR applications in geological hazard monitoring and deformation assessment.

The application of multi-temporal interferometric synthetic aperture radar (MTInSAR) technology in bridge structural health monitoring often encounters considerable challenges due to the intricate nature of bridge structures. Notably, the thermal expansion and contraction (TEC) of bridges can lead to prominent interferometric phase jumps at the expansion joints. When the magnitude of the phase jump exceeds π, the continuity assumption required for phase unwrapping is no longer valid. To address this limitation, we propose an adaptive MTInSAR method that can partition the bridge into independent segments and concurrently estimate deformation from multiple reference points. We validate the effectiveness of the method using 23 TerraSAR-X images of the Shanghai Yangtze River Bridge. The results demonstrate the successful detection of expansion joints and reliable phase unwrapping in PS sub-networks.

The application of multitemporal interferometric synthetic aperture radar (MTInSAR) technology in bridge structural health monitoring often encounters considerable challenges due to the intricate nature of bridge structures. Notably, the thermal expansion and contraction (TEC) of bridges can lead to prominent interferometric phase jumps at the expansion joints. When the magnitude of the phase jump exceeds$\pi $, the continuity assumption required for phase unwrapping is no longer valid. Consequently, classical phase unwrapping methods fail to accurately retrieve bridge deformation. To address this limitation, we propose an adaptive MTInSAR method that can partition the bridge into independent segments and concurrently estimate deformation from multiple reference points. The algorithm first identifies expansion joint locations using a mean square error threshold. Subsequently, reference point selection and segmental phase unwrapping are performed to derive displacement time series of persistent scatterers (PSs), where the mechanical properties of the bridge structure are considered. We validate the effectiveness of the method using 23 TerraSAR-X (TSX) images of the Shanghai Yangtze River Bridge. The results demonstrate the successful detection of expansion joints and reliable phase unwrapping in PS subnetworks. Moreover, a comparative analysis with the classical minimum cost flow (MCF) method highlights the superior adaptability and reliability of the proposed approach. Finally, threshold values for triggering conditions when phase jumps occur are quantified. The proposed work will enhance the robust monitoring of bridge motions, safeguarding the structural health of bridges.

Coherence estimation is crucial in Interferometric Synthetic Aperture Radar (InSAR) for various applications, including land cover classification, change detection, and multi-temporal InSAR techniques. However, estimation challenges often arise due to systematic phases caused by deformation and topography, leading to an underestimation. Existing FFT-based stripe correction methods have limitations in handling complex patterns and are noise-sensitive. We propose here a novel approach using local phase surface fitting to remove the trend component and thereby improve the accuracy of the coherence estimation. The algorithm involves adaptive window size selection based on varying phase patterns and joint estimation of surface model parameters using regional network adjustment. Comparative experiments with simulated and Sentinel-1A data demonstrate the superiority of the method in effectively removing trend components, especially from nonlinear stripe regions. This improvement is evident in the significantly enhanced average coherence, with increases of 37.4% and 60.1% observed in the two experimental areas, resulting in enhanced quality of interferogram coherence maps.

In multitemporal interferometric synthetic aperture radar (MTInSAR) processing, phase unwrapping (PhU) is a vital procedure, which affects the accurate deformation retrieval, especially in environments suffering decorrelation. Although a great surge of work focuses on solving the integers of$2\pi $associated with the wrapped observations (i.e., the inputs of unwrapping algorithms), the quality of inputs deserves an equal attention, as it is a basis for a reliable unwrapping. In this letter, we seek to improve the PhU accuracy by enhancing the entire quality of differential phase observations. To select an optimal interferogram stack efficiently, we propose a quadtree-based coherence estimation method for fast evaluating the interferogram quality and then develop a strategy that constructs redundant networks connecting synthetic aperture radar (SAR) images and points, respectively. The proposed strategy utilizes the combination of minimum spanning tree (MST) and triangular closure to determine the pair of image/point included in the network. We validate the effectiveness of our method by Sentine-1 SAR data over Shenzhen airport, where decorrelated scatterers with weak backscattering energy in runways challenge a reliable subsidence extraction. The cross-comparison indicates the importance of the quality of inputs that affects the point connectivity in both temporal and spatial dimensions.

With well-controlled orbits and a more accurate timing system of the new-generation synthetic aperture radar (SAR) satellites, the ability of high-precision geolocation with multiple SAR acquisitions has been verified based on radar reflectors. In this letter, SAR absolute and differential geolocation methods are introduced and implemented to retrieve the coordinates of two different types of radar reflectors: corner reflectors (CRs) and multidirectional dihedral reflectors (MDRs). The experimental results demonstrate that decimeter- even centimeter-level positioning accuracy can be obtained by SAR stereo geolocation based on multiaspect SAR acquisitions from RadarSAT-2 (RS-2), COSMO-SkyMed (CSK), Sentinel-1 (S1), and TerraSAR-X (TSX), respectively.

The observation model of multitemporal inteferometric synthetic aperture radar (MTInSAR) is an underdetermined system. To obtain a unique solution, the traditional techniques impose the temporal constraints by assuming the deformation pattern typically as, e.g., a linear or polynomial model. However, these temporal constraints are not necessarily compatible with the realistic deformation, especially for complex deformations of, e.g., landslides and permafrost. Such discrepancy will bias the retrieval of MTInSAR parameters, thus producing inaccurate deformation results. In this letter, we propose a method for directly solving the deformation sequence by imposing the spatial similarity constraints instead of temporal constraints. The underlying rationale is that the spatially closer points share more similar deformation patterns for most motion events. The capability of the proposed method for retrieving displacement is initially demonstrated by using both simulated and real data experiments.

Differential interferometric synthetic aperture radar (DInSAR) has been widely used as one of the most important technologies for determining coseismic deformation. However, DInSAR processing is often perturbed by errors including atmospheric effects and those in topographic models, SAR satellite orbits, and phase unwrapping operation. These nuisance components can degrade the accuracy of the measurements and, therefore, distort the inversion of fault slips especially for moderate earthquakes. We propose in this letter a multitemporal InSAR (MTInSAR) method aiming to accurately determine coseismic deformation. By jointly analyzing a set of preseismic SAR images and one postseismic image, the method allows effective separation of coseismic deformation from topographic and satellite orbital errors deformation based on the distinct spatio-temporal characteristics of the signals. Since the solution is achieved directly from wrapped differential phases, the retrieved deformation is also immune to phase unwrapping errors. The October 6, 2008 Mw 6.3 Dangxiong, China earthquake is studied with the proposed method as an example. The slip inverted, respectively, from the MTInSAR and DInSAR coseismic deformation measurements shows up to 34-cm differences, indicating that the topographic error and inaccurate removal of orbital errors can bias the fault slip inversion.

Estimation of surface deformation using synthetic aperture radar interferometry (InSAR) technique requires a precise removal of the topographic phase. Under multitemporal InSAR (MTInSAR) framework, topographic residual raised by differential operation with external Digital Elevation Model (DEM) is usually parameterized and jointly estimated together with deformation model, while the estimation can be distorted by systematic errors (e.g., model bias, baseline error). This letter aims to offer practical guidelines to users of MTInSAR framework concerning these errors and estimation precision. Starting from the generalized model, we derived the error propagation formula to quantitatively indicate how and to what extent the systematic errors degrade the topographic parameter estimation. The formulas validated by simulated tests are expected to be useful for optimal selection of MTInSAR modeling strategies and development of innovative algorithms (e.g., non-parametric estimator) for retrieval of DEM residuals from MTInSAR measurements.

Phase decorrelation, as one of the main error sources, limits the capability of interferometric synthetic aperture radar (InSAR) for deformation mapping over areas with low coherence. Although several methods have been realized to reduce decorrelation noise, for example, by phase linking and spatial and temporal filters, their performances deteriorate when coherence estimation bias exists. We present an arc-based approach that allows reconstructing unwrapped interval phase time-series based on iterative weighted least squares (WLS) in temporal and spatial domains. The main features of the method are that phase optimization and unwrapping can be jointly conducted by spatial and temporal iterative WLS and coherence matrix bias has negligible effects on the estimation. In addition, the linear formation makes the implementation suitable with small subset of interferograms, providing an efficient solution for future big SAR data. We demonstrate the effectiveness of the proposed method using simulated and real data with different decorrelation mechanisms and compare our approach with the state-of-art phase reconstruction methods. Substantial improvement can be achieved in terms of reduced root-mean-square error (RMSE) in the simulation data and increased density of coherent measurements in the real data.

Deformation monitoring of a converter station of an electrical power transmission system will help to prevent potential damages to power facilities and properties. Corner reflector InSAR (CRInSAR) enables local deformation measurements in low coherence areas like construction-engineering projects. However, the accuracy of CRInSAR will be degraded by the phase unwrapping errors, especially when the deformation is large or dominated by nonlinear component. This letter reports a study that employs CRInSAR technique to monitor the deformations of ten CRs installed in Xiangtan converter station, China, with seven TerraSAR-X Spotlight images. A two-step phase unwrapping tactics is proposed based on the least squares ambiguity decorrelation adjustment (LAMBDA) algorithm to focus on estimating nonlinear deformation without being affected by unwrapping errors. The results reveal that the two-step LAMBDA algorithm can achieve an accuracy of less than 2 mm for CRInSAR deformation monitoring regardless of small- or large-scale deformations, as validated by the trigonometric leveling measurements.

Tatun volcano group, the last active volcano in Taiwan, is located in northern Taipei Basin, only 15 km north of the Taipei City. It was previously thought to be a dead volcano, but recent studies show that the last magmatic eruption happened about 5000 to 6000 years ago. The geothermal and seismic activities over the Tatun volcanic area have been highly active in recent years. The geochemical analysis implies the potential existing of the magma chamber under the ground surface of northern Taiwan which has the possibility of re-eruption in the future. In this study, we use ALOS-1/PALSAR images to monitor the surface deformation at the Tatun volcanic area. Stratified atmospheric delay and orbit errors are well considered and corrected by an adaptive patch-based method. The derived displacement history provides a detailed map of surface change with large spatial extent, which is validated by GPS measurements. The results demonstrate the capability of InSAR technique to monitor surface deformation over the volcanic zones.

Tropospheric delays (TDs) in differential interferometric synthetic aperture radar (InSAR) measurements are mainly caused by spatial and temporal variation of pressure, temperature, and humidity between SAR acquisitions. These delays are described as one of the primary error sources in InSAR observations. Although independent atmospheric measurements have been used to correct TDs, their sparse spatial or temporal resolution requires interpolation, leading to uncertainties in the corrected interferograms. The performance of the conventional phase-based correction method is weakened by the presence of confounding signals (e.g., TDs, deformation, and topographic errors) and spatial variability of the troposphere. Here, we propose a method that can simultaneously estimate stratified TDs together with parameters of deformation and topographic error based on their distinct spatial-temporal correlation. Spatial variability of the relationship between TDs and topographic height is addressed through localized estimation in windows divided by quadtree according to height gradient. We demonstrate the performance of the proposed method with both simulated and real data sets. In addition, both advantages and disadvantages of this method are addressed.

Isolating phase residuals due to inaccurate external digital elevation model (DEM) is important in retrieval and interpretation of deformation behavior from interferometric synthetic aperture radar (InSAR) observations. Multitemporal InSAR (MTInSAR), by taking DEM error as a parameter, can make the isolation possible. However, due to the presence of atmospheric artifacts in observations and improper deformation model employed in the observation system, accurate retrieval of DEM error cannot be guaranteed in current MTInSAR techniques. Considering that the DEM error has a fixed spatial pattern and its contribution to interferometric phase-only changes with spatial baselines, we propose here a nonparametric method that can estimate the DEM error in a more robust way. To retrieve signals having a fixed spatial pattern from unwrapped MTInSAR measurements, the independent component analysis (ICA) is used. Experiments with synthetic and real data sets indicate the proposed method is able to estimate DEM error with no a priori information about deformation. Moreover, experiments also show that the method can provide a more robust estimation when the observed phase observations are affected by atmospheric delays and/or the number of interferograms used is limited.

Coherent point (including persistent and distributed scatterers) selection and phase ambiguity treatment (or parameter estimation) are the key tasks involved in multitemporal InSAR (MTInSAR) algorithms, which are usually conducted separately with empirical thresholds. It is not rare to see that due to the discrepancies on threshold setting, even for the same MTInSAR technique with the same data sets, it will raise different (sometimes quite notable) results and affect the applicability of InSAR techniques. We propose here an integrated MTInSAR estimator that combines the coherent point selection and phase vector unwrapping into a single step. Essentially, the estimator aims to recover the unwrapped phase vector at coherent points. Therefore, it could serve as an alternative solution of spatial-temporal phase unwrapping problem. In the estimator, wrapped phase at all pixels in short baseline interferograms are taken as observations. Starting from the phase differences at arcs of a fully connected network of pixels, based on the residual analysis and spatial closure of phase triangularity, the estimator can detect and delete the arcs having unacceptable phase noise and phase ambiguities. By integrating the phase differences at the remained arcs, the unwrapped phase at coherent points in consecutive acquisition intervals can be obtained. Impressively, the estimator is immune to the bias raised by improper deformation model. The performance of the proposed estimator is evaluated via semisynthetic and real data tests. Considering that the phase enhancement algorithms (e.g., phase-linking and Extended Minimum Cost Flow-Small BAseline Subset) that can reconstruct high-quality wrapped phases are gaining popularity, the proposed estimator can also be implemented as a postprocessing module of these algorithms for retrieval of unwrapped phase vectors at coherent points.

Removing the topographic component in the interferometric synthetic aperture radar (InSAR) phase is conventionally conducted using an external digital elevation model (DEM). However, with an increasing spatial resolution of SAR data, the external DEM is becoming less qualified for this purpose, resulting in notable phase residues and even decorrelation in differential interferograms. Although topographic residuals can be parameterized and estimated by multi-temporal InSAR (MTInSAR) techniques, its accuracy is limited by several factors. Instead of providing accurate height information, shortening the length of baselines is an alternative for DEM phase mitigation. We propose here an MTInSAR processing framework that can retrieve the deformation time series without the estimation of topographic residuals. Within the framework, we generate a set of pseudo interferograms with near-zero baselines by integer combination and take these pseudo interferograms as observations of MTInSAR model, where deformation becomes the only signal that needs to be parameterized. The deformation time series is then retrieved directly from wrapped phases by ridge estimation with an integer ambiguity detector. It is noted that although atmospheric artifacts might be magnified during the combination, their differential components at arcs constructed with neighboring points that are not significantly enlarged. The proposed method is particularly suitable for infrastructure deformation monitoring in urban areas where no accurate external DEM is available. It also has promising potential for retrieving deformation from SAR data stacks with short acquisition intervals since the combination can enlarge the signal of interests in pseudo-observations. Semisynthetic and real data tests indicate that the proposed method has satisfied performance on DEM error mitigation and deformation time series estimation.

Conventional synthetic aperture radar (SAR) image formation requires uniform sampling along the azimuth direction. These image formation relies on frequency domain algorithms including the Range-Doppler Algorithm (RDA), Chirp-Scaling Algorithm (CSA) [1] etc, that make use of azimuth Fast Fourier Transform, hence the requirement of uniform sampling. While uniform sampling in space is not always achievable, the samples can be interpolated onto a uniform grid given the sampling rate is Nyquist. This paper studies the effect of SAR image formation when the azimuth sampling is not uniform, and not Nyquist in some interval. The result showed that even if there is a wide interval in the middle of the synthetic aperture with no samples, an image can still be formed. This result could be useful when the SAR antenna is a phased array, or when the hardware is generating bursts of pulses followed by a quiet window.

Karachi is located on southernmost border of Pakistan along the Arabian Sea coast. Concerned institutions fear the occurrence of subsidence in the city, further contributing to the relative sea level rise. No direct measurement has been made so far about the subsidence rate and its contribution to city's submergence risk. Our study presents first and preliminary results of vertical ground deformation measurement over this area using an advanced Temporarily Coherent Point InSAR technique using Envisat/Asar and Sentinel-l A data. These datasets allowed us to study deformation in this area from 2004-2016, with some data gaps, thus providing a long -term analysis. Results show that various parts of the city are unstable and undergoing deformation of up to about 15 mm/yr. However, we could not find significant correlation between faults passing through the city and the deformation in its different parts. Future studies should focus on monitoring the deformation on a regular basis.

Stratified tropospheric delays (TDs) in differential interferometric synthetic aperture radar (InSAR) result from the temporal variation of vertical stratification in the lower part of the troposphere. Although an approximately model can be made by assuming a linear relationship between topography and delayed phase in the interferogram, the estimation is weakened by the spatial variability of troposphere and the interference from other confounding signals (e.g., deformation, topographic error and orbit error, etc.). In this contribution, a jointly tropospheric correction scheme is proposed to simultaneously estimate stratified tropospheric delays with deformation and topographic errors. Spatial variability of tropospheric properties is addressed through a localized estimation which is derived by quadtree segmentation according to height gradient. The performance of the proposed method is validated and compared with the conventional linear and weather-model-based methods using Sentinel-1 dataset.

Topographic residuals in differential interferometric synthetic aperture radar (InSAR) measurements are mainly caused by inaccurate external digital elevation model (DEM). Accurate separation of the phase component contributed by topographic residuals plays an important role in the retrieval of deformation time series from InSAR observations. Even though the residuals can be modeled and estimated in the framework of multitemporal SAR interferometry (MTInSAR), it is not clear what an optimal processing strategy is and how accurate the estimation can reach. We analyze here the factors that affect the accuracy of the retrieved DEM residuals by applying four commonly used MTInSAR methods in a series of simulated scenarios. The results indicate that besides the quality of interferometric observations, the thresholds of spatial and temporal baselines, the diversity of spatial baseline lengths, the connectivity of interferogram network, and improper deformation model also fluctuate the accuracy of the retrieved topographic residuals. According to these affecting factors, this paper sheds light on an optimal approach to reliably retrieve accurate topographic residuals under MTInSAR framework.

A new approach is presented for mapping 3-D surface displacement caused by subsurface fluid volumetric change based on 1-D interferometric synthetic aperture radar (InSAR) line-of-sight measurements and surface deformation modeling. The relationship between surface deformation and source fluid volumetric change is modeled according to elastic half-space theory. A distinctive advantage of the proposed approach is that it effectively extends the capability of the sun-synchronous orbit side-looking synthetic aperture radar that has been essentially only able to measure 1-D displacements accurately or at most 2-D displacements when InSAR measurements from more than one orbit or platform are combined. Experimental studies are carried out with both simulated and real data sets to test the performance of the method. The results have demonstrated that the approach works very well.

Orbital errors, characterized typically as longwavelength artifacts, commonly exist in interferometric synthetic aperture radar (InSAR) imagery as a result of inaccurate determination of the sensor state vector. Orbital errors degrade the precision of multitemporal InSAR products (i.e., ground deformation). Although research on orbital error reduction has been ongoing for nearly two decades and several algorithms for reducing the effect of the errors are already in existence, the errors cannot always be corrected efficiently and reliably. We propose a novel model that is able to jointly estimate deformation rates and orbital errors based on the different spatial-temporal characteristics of the two types of signals. The proposed model is able to isolate a long-wavelength ground motion signal from the orbital error even when the two types of signals exhibit similar spatial patterns. The proposed algorithm is efficient and requires no ground control points. In addition, the method is built upon wrapped phases of interferograms, eliminating the need of phase unwrapping. The performance of the proposed model is validated using both simulated and real data sets. The demo codes of the proposed model are also provided for reference.

A Kalman-filter-based approach is presented for resolving 3-D surface displacements using multisensor, multitrack, and multitemporal interferometric synthetic aperture radar (SAR) measurements. Measurements from each interferogram are projected into the three reference directions and combined in the Kalman filter model with displacements determined from previous interferograms to produce updated displacement measurements. Both simulated and real data sets are used to test the proposed approach. It is found that the method works well when the measurement noise is low. The displacements in the north direction, however, are much lower in accuracy than those in the other two directions and even become unstable when the measurement noise is high due to the polar-orbiting imaging geometries of the current satellite SAR sensors.

The European Space Agency's Sentinel-1, a C-band imaging radar mission to be launched in mid-2013, will provide a continuity of radar data for monitoring the changing Earth. The azimuth resolution of Sentinel-1's background mode, interferometric wide-swath (IW) mode, is four times lower than that of European remote-sensing satellite (ERS) and Envisat systems. Therefore, the measurement accuracy of along-track displacement from Sentinel-1 IW images presumably will be significantly reduced. In this paper, we test the feasibility of along-track displacement measurement from Sentinel-1 IW mode. We simulate Sentinel-1 IW synthetic aperture radar (SAR) images from the ERS raw data that captured the coseismic deformation of the 1999 Hector Mine earthquake in California. Along-track displacement maps are generated using multiple-aperture interferometric SAR (MAI) and intensity tracking techniques, respectively, and are compared with GPS measurements. The root-mean-square (rms) error between the synthetic Sentinel-1 MAI and GPS measurements is about 9.6 cm, which corresponds to only 0.5 % of the azimuth resolution. The rms error between the along-track displacements from synthetic Sentinel-1 offset tracking and GPS is about 27.5 cm, which is about 1.4 % of the azimuth resolution. These results suggest that the MAI method will still be useful to measure along-track displacements from Sentinel-1 IW InSAR imagery and that it would be difficult to effectively measure the along-track displacements by the Sentinel-1 offset tracking method.

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.

In this paper, we propose a least-squares-based method for multitemporal synthetic aperture radar interferometry that allows one to estimate deformations without the need of phase unwrapping. The method utilizes a series of multimaster wrapped differential interferograms with short baselines and focuses on arcs at which there are no phase ambiguities. An outlier detector is used to identify and remove the arcs with phase ambiguities, and a pseudoinverse of the variance-covariance matrix is used as the weight matrix of the correlated observations. The deformation rates at coherent points are estimated with a least squares model constrained by reference points. The proposed approach is verified with a set of simulated data.