Phase Unwrapping Errors Research Articles

Pixel-Wise Phase Unwrapping With Adaptive Reference Phase Estimation for 3-D Shape Measurement

Phase unwrapping plays an important role in phase-based three-dimensional (3D) shape measurement. This paper proposes an effective pixel-wise phase unwrapping method without requiring additional fringe patterns. Firstly, compared with the geometric constraint-based (GCB) method which needs calibrate the fringe projection system and create a reference phase at the closest plane <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z_min</i> within the measurement volume, the proposed method can adaptively and directly estimate the reference phase from the wrapped phase without system calibration and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z_min</i> estimation. Secondly, based on the finding that the slope angle of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z_min</i> plane ignored by the GCB method has significant impact on the measurement range, thus the phase gradients that highly correlates with the optimal slope angle are involved into reference phase estimation. The wrapped phase can be pixel-by-pixel unwrapped by comparing with the reference phase. Both simulations and experiments have been conducted to demonstrate the efficiency of the proposed method. Compared with traditional two-frequency method and phase-coding method, the proposed method can improve the measuring speed by 2 times. Experiment results show that the proposed method can effectively remove the phase unwrapping errors and achieve the mean absolute phase error of 0.0137 rad, which has obvious advantages relative to traditional methods.

Detecting slow-moving landslides using InSAR phase-gradient stacking and deep-learning network

Landslides are a major geohazard that endangers human lives and properties. Recently, efforts have been made to use Synthetic Aperture Radar Interferometry (InSAR) for landslide monitoring. However, it is still difficult to effectively and automatically identify slow-moving landslides distributed over a large area due to phase unwrapping errors, decorrelation, troposphere turbulence and computational requirements. In this study, we develop a new approach combining phase-gradient stacking and a deep-learning network based on YOLOv3 to automatically detect slow-moving landslides from large-scale interferograms. Using Sentinel-1 SAR images acquired from 2014 to 2020, we developed a burst-based, phase-gradient stacking algorithm to sum up phase gradients in short-temporal-baseline interferograms along the azimuth and range directions. The stacked phase gradients clearly reveal the characteristics of localized surface deformation that is mainly caused by slow-moving landslides and avoids the errors due to phase unwrapping in partially decorrelated areas and atmospheric effects. Then, we trained the improved Attention-YOLOv3 network with stacked phase-gradient maps of manually labeled landslides to achieve quick and automatic detection. We applied our method in an ∼180,000 km2 area of southwestern China and identified 3,366 slow-moving landslides. By comparing the results with optical imagery and previously published landslides in this region, the proposed method can achieve automatic detection over a large area precisely and efficiently. From the derived landslide density map, we determined that most landslides are distributed along the three large rivers and their branches. In addition to some counties with known high-density landslides, approximately 10 more counties with high landslide density were exposed, which should attract more attention to their risks for geohazards. This application demonstrates the potential value of our newly developed method for slow-moving landslide detection over a nation-wide area, which can be employed before applying more time-consuming time-series InSAR analysis.

Supervised Machine Learning Algorithms for Ground Motion Time Series Classification from InSAR Data

The increasing availability of Synthetic Aperture Radar (SAR) images facilitates the generation of rich Differential Interferometric SAR (DInSAR) data. Temporal analysis of DInSAR products, and in particular deformation Time Series (TS), enables advanced investigations for ground deformation identification. Machine Learning algorithms offer efficient tools for classifying large volumes of data. In this study, we train supervised Machine Learning models using 5000 reference samples of three datasets to classify DInSAR TS in five deformation trends: Stable, Linear, Quadratic, Bilinear, and Phase Unwrapping Error. General statistics and advanced features are also computed from TS to assess the classification performance. The proposed methods reported accuracy values greater than 0.90, whereas the customized features significantly increased the performance. Besides, the importance of customized features was analysed in order to identify the most effective features in TS classification. The proposed models were also tested on 15000 unlabelled data and compared to a model-based method to validate their reliability. Random Forest and Extreme Gradient Boosting could accurately classify reference samples and positively assign correct labels to random samples. This study indicates the efficiency of Machine Learning models in the classification and management of DInSAR TSs, along with shortcomings of the proposed models in classification of nonmoving targets (i.e., false alarm rate) and a decreasing accuracy for shorter TS.

A hybrid method for MT-InSAR phase unwrapping for deformation monitoring in urban areas

• A hybrid method is proposed to enhance the phase unwrapping of MT-InSAR in urban. • Consideration of the impact of building height and spatial network structure. • Improvements in phase unwrapping allow for better geocoding of coherent points. The accuracy of phase unwrapping in multi-temporal interferometric synthetic aperture radar (MT-InSAR) technology affect closely on the accuracy of ground deformation monitoring. In the urban area, urban infrastructures such as high-rise buildings present additional challenges to phase unwrapping due to the sudden elevation changes. The failure rate of phase unwrapping is often much higher in such areas, bringing more biases to the estimated deformation and height values. We propose a new method for MT-InSAR phase unwrapping especially for deformation monitoring in urban areas. The method isolates the propagation path of information by considering the building height information of a study area. Two quality controllers are also developed to refine the arc observation network structure for network adjustment and to correct the phase unwrapping errors. The proposed method is tested using both simulated and real datasets. The results show that the building height and the geolocation of the coherence points were estimated much more accurately, demonstrating the effectiveness of the proposed method in monitoring deformation of urban area.

INSAR DEFORMATION TIME SERIES CLASSIFICATION USING A CONVOLUTIONAL NEURAL NETWORK

Abstract. Temporal analysis of deformations Time Series (TS) provides detailed information of various natural and humanmade displacements. Interferometric Synthetic Aperture Radar (InSAR) generates millimetre-scale products, indicating the chronicle behaviour of detected targets via TS products. Deep Learning (DL) can handle a massive load of InSAR TS to categorize significant movements from non-moving targets. To this end, we employed a supervised Convolutional Neural Network (CNN) model to distinguish five deformations trends, including Stable, Linear, Quadratic, Bilinear, and Phase Unwrapping Error (PUE). Considering several arguments in a CNN model, we trained numerous combinations to explore the most accurate combination from 5000 samples extracted from a Persistent Scatterer Interferometry (PSI) technique and Sentinel-1 images over the Granada region, Spain. The model overall accuracy exceeds 92%. Deformations of three cases of landslides were also detected over the same area, including the Cortijo de Lorenzo, El Arrecife, and Rules Viaduct areas.

Using Range Split-Spectrum Interferometry to Reduce Phase Unwrapping Errors for InSAR-Derived DEM in Large Gradient Region

The use of the conventional interferometric synthetic aperture radar (InSAR) to generate digital elevation models (DEMs) always encounters phase unwrapping (PU) errors in areas with a sizeable topographic gradient. Range split-spectrum interferometry (RSSI) can overcome this issue; however, it loses the spatial resolution of the SAR image. We propose the use of the RSSI-assisted In-SAR-derived DEM (RID) method to address this challenge. The proposed approach first applies the RSSI method to generate a prior DEM, used for simulating terrain phases. Then, the simulated terrain phases are subtracted from the wrapped InSAR phases to obtain wrapped residual phases. Finally, the residual phases are unwrapped by the minimum cost flow (MCF) method, and the unwrapped residual phases are added to the simulated phases. Both the simulated and TerraSAR-X data sets are used to verify the proposed method. Compared with the InSAR and RSSI methods, the proposed approach can effectively decrease the PU errors of large gradients, ensure data resolution, and guarantee the DEM’s accuracy. The root mean square error between the topographic phase simulated from the real DEM and the topographic phase generated from the proposed method is 2.22 rad, which is significantly lower than 6.60 rad for InSAR, and the improvement rate is about 66.36%.

Refined InSAR tropospheric delay correction for wide-area landslide identification and monitoring

SAR Interferometry (InSAR) proves to be effective for investigating landslides. However, its measurement accuracy is largely limited by the complex atmospheric delay distortion in alpine valley regions, resulting in poor performance of landslides detection and monitoring. Particularly, the spatial atmospheric heterogeneity over wide areas cannot be accurately reflected by conventional empirical phase-elevation models or external data-based methods. In this study, we proposed a multi-temporal moving-window linear model (MMLM) to correct the tropospheric delay for wide-area landslides investigation. This is a linear regression model based on the elevation-phase relationship for modeling multi-temporal phases within a sliding local window. It mitigates the influence of local turbulent phase, local landslide deformation, and phase unwrapping error on parameter estimation, providing precise heterogeneous atmospheric corrections for wide-area InSAR landslide identification and monitoring. A simulation experiment was conducted to analyze the sensitivity of model parameters settings and evaluate the effectiveness of the MMLM model. Furthermore, we demonstrated the performance of the MMLM model through a comparison with the ERA5, GACOS, spatial-temporal filtering, and traditional linear model using descending and ascending Sentinel-1 data over the reservoir area of the Lianghekou hydropower station. Among the above-mentioned methods, the standard deviation of original unwrapped phases achieved the largest decrease of more than 35% and 50% after correction by the MMLM model for the descending and ascending Sentinel-1 tracks, respectively. In addition, the accurate deformation corrected by the MMLM model improved the landslides investigation, not only can help for delineating landslide boundaries in space but also retrieving movement evolution in time.

Analysis of strain estimation methods in phase-sensitive compression optical coherence elastography.

In compression optical coherence elastography (OCE), deformation is quantified as the local strain at each pixel in the OCT field-of-view. A range of strain estimation methods have been demonstrated, yet it is unclear which method provides the best performance. Here, we analyze the two most prevalent strain estimation methods used in phase-sensitive compression OCE, i.e., weighted least squares (WLS) and the vector method. We introduce a framework to compare strain imaging metrics, incorporating strain sensitivity, strain signal-to-noise ratio (SNR), strain resolution, and strain accuracy. In addition, we propose a new phase unwrapping algorithm in OCE, fast phase unwrapping (FPU), and combine it with WLS, termed WLSFPU. Using the framework, we compare this new strain estimation method with both a current implementation of WLS that incorporates weighted phase unwrapping (WPU), termed WLSWPU, and the vector method. Our analysis reveals that the three methods provide similar strain sensitivity, strain SNR, and strain resolution, but that WLSFPU extends the dynamic range of accurate, measurable local strain, e.g., measuring a strain of 2.5 mɛ with ∼4% error, that is ×11 and ×15 smaller than the error measured using WLSWPU and the vector method, respectively. We also demonstrate, for the first time, the capability to detect sub-resolution contrast in compression OCE, i.e., changes in strain occurring within the strain axial resolution, and how this contrast varies between the different strain estimation methods. Lastly, we compare the performance of the three strain estimation methods on mouse skeletal muscle and human breast tissue and demonstrate that WLSFPU avoids strain imaging artifacts resulting from phase unwrapping errors in WLSWPU and provides improved contrast over the other two methods.

Phase unwrapping algorithm based on phase edge tracking for dynamic measurement.

Phase unwrapping is an essential procedure for fringe projection profilometry (FPP). To improve measurement efficiency and reduce phase unwrapping errors (PUEs) in dynamic measurement, a phase unwrapping algorithm based on phase edge tracking is proposed, which unwraps the current wrapped phase map with the aid of the previously unwrapped one. The phase edges are accurately tracked and their trajectories are used to divide the phase map into several regions, each of which is unwrapped either temporally or spatially according to its properties. It doesn't require extra patterns for phase unwrapping once the initial unwrapped phase map is obtained, thus significantly increasing the frame rate of the 3D result. Meanwhile, it greatly reduces the PUEs caused by noise amplification and motion-induced misalignment of phase edges. Experiments prove that it is capable of retrieving the absolute phase maps of complex dynamic scenes with high unwrapping accuracy and efficiency.

Phase error analysis and unwrapping error suppression in phase-sensitive optical time domain reflectometry.

Phase-sensitive optical time domain reflectometry becomes an effective tool to realize distributed sensing, and the optical phase of the received light is usually used to quantify the strain for both dynamic and static measurement. The analysis on the overall phase error has been improved by considering the proportionality of the detection noise to the local optical power. The estimation accuracy is greatly improved by using the proposed theory, the probability density of the estimation accuracy over 99% is > 0.6, ∼39 times larger than the previously reported method. The phase unwrapping may malfunction due to the noisy signal, causing large phase errors. Point break detection algorithms are used to locate the incorrect phase unwrapping points, so the temporal evolution of the phase retrieved at each position can be divided into several sections with different offset. The phase unwrapping error is then suppressed by removing the offset.

Spatio-Temporal Quality Indicators for Differential Interferometric Synthetic Aperture Radar Data

Satellite-based interferometric synthetic aperture radar (InSAR) is an invaluable technique in the detection and monitoring of changes on the surface of the earth. Its high spatial coverage, weather friendly and remote nature are among the advantages of the tool. The multi-temporal differential InSAR (DInSAR) methods in particular estimate the spatio-temporal evolution of deformation by incorporating information from multiple SAR images. Moreover, opportunities from the DInSAR techniques are accompanied by challenges that affect the final outputs. Resolving the inherent ambiguities of interferometric phases, especially in areas with a high spatio-temporal deformation gradient, represents the main challenge. This brings the necessity of quality indices as important DInSAR data processing tools in achieving ultimate processing outcomes. Often such indices are not provided with the deformation products. In this work, we propose four scores associated with (i) measurement points, (ii) dates of time series, (iii) interferograms and (iv) images involved in the processing. These scores are derived from a redundant set of interferograms and are calculated based on the consistency of the unwrapped interferometric phases in the frame of a least-squares adjustment. The scores reflect the occurrence of phase unwrapping errors and represent valuable input for the analysis and exploitation of the DInSAR results. The proposed tools were tested on 432,311 points, 1795 interferograms and 263 Sentinel-1 single look complex images by employing the small baseline technique in the PSI processing chain, PSIG of the geomatics division of the Centre Tecnològic de Telecomunicacions de Catalunya (CTTC). The results illustrate the importance of the scores—mainly in the interpretation of the DInSAR outputs.

Classification of ground deformation using sentinel-1 persistent scatterer interferometry time series

ABSTRACT Displacement time series (TS) provides temporal and spatial information related to ground deformation. This study aims to investigate temporal behavior of ground deformation TS, including classification of displacement trends and periodicity evaluation, which ease the interpretation of movements. To this end, we propose several modifications to an existing automatic classification workflow of Persistent Scatterers Interferometry (PSI) TS using new tests to classify ground deformations into seven main trends: Stable, Linear, Quadratic, Bilinear, Phase Unwrapping Errors (PUE), Discontinuous with constant and different velocities. We illustrate our approach over 1500 km2 of the Granada region and the metropolitan area of Barcelona, which were monitored using Sentinel-1 images and a PSI technique. This study provided the spatial distribution of different ground movement types and was useful to detect several TS anomalies due to PUE. The proposed approach also identified stable targets, which were wrongly classified as moving scatterers by the existing classification method. A periodicity analysis was finally performed using the Welch’s power spectral density estimator to investigate seasonal and yearly fluctuations. The method was validated using simulated data, where the classified TSs characterized by probable phase unwrapping errors were verified by PSI experts. The overall classification accuracy was 77.8%, indicating that the proposed method has a considerable TS classification potential.

Ground Movement Classification Using Statistical Tests Over Persistent Scatterer Interferometry Time Series

This study proposes modifications to an existing automatic classification method of Persistent Scatterers Interferometry (PSI) time series (TS) and a new procedure to classify ground movements into seven classes. We also represent a technique to detect TSs affected by phase unwrapping errors and a reclassification part to detect stable points, which are incorrectly classified as moving points using the original method. Around 60 km2 of Catalunya were classified using Sentinel-1 images and a PSI technique. The proposed method classified 78359 PS TS. This study provided the spatial distribution of ground movement classes and detected several time series anomalies.

InSAR Phase Unwrapping Error Correction for Rapid Repeat Measurements of Water Level Change in Wetlands

Here, we present an enhanced algorithm to correct interferometric synthetic aperture radar (InSAR) phase unwrapping errors by incorporating iterative spatial bridging between islands and phase closure among interferograms. We use rapid repeat airborne synthetic aperture radar acquisitions from NASA’s airborne uninhabited aerial vehicle synthetic aperture radar (UAVSAR) instrument to estimate short-term changes in water level within coastal wetlands from a stack of consecutive interferograms acquired with very short temporal separation (~30 min). The algorithm is applied to six consecutive UAVSAR images collected in tidal wetlands of the Wax Lake Delta, Louisiana, USA. Validation of our water level change retrievals with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> field observations was conclusive with high correlation and an RMSE generally smaller than 3 cm. Comparison of our algorithm with other phase unwrapping error correction methods shows significant improvement (30%–35% increase in the number of correctly unwrapped pixels) when applied to rapid changes in water level. The set of corrections presented in this work enables measurement of water level change in deltas and other areas where tides drive highly dynamic flooding of inland vegetated areas. Although demonstrated for water level change, the method is applicable to other InSAR datasets with large spatial gradients or observed discontinuities between coherent but spatially isolated areas.

On the Phase Nonclosure of Multilook SAR Interferogram Triplets

This work explores the properties characterizing the phase non-closure of multi-look synthetic aperture radar (SAR) interferograms. Specifically, we study the implications of multi-look phase time incongruences on the generation of ground displacement time-series through small baseline (SB) multi-temporal InSAR (Mt-InSAR) methods. Our research clarifies how these phase inconsistencies can propagate through a time-redundant network of SB interferograms and contribute, along with phase unwrapping (PhU) errors, to the quality of the generated ground displacement products. Moreover, we analyze the effects of short-lived phase bias signals that could happen in sequences of short baseline (SB) interferograms and propose a strategy for their mitigation. The developed methods have been tested using both simulated and real SAR data. The latter were collected by the Sentinel-1A/B (C-band) sensors over the study areas of Nevada state, U.S., and Sicily Island, Italy.

An Orbital Error Correction Model Based on Triplet Network and Shrunken Estimation

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 integrates <i>L</i>²-Norm with <i>L</i>¹-Norm regularization, also known as Lasso regularization. The rationale behind it is to first determine the initial orbital parameters by utilizing the traditional polynomial-based method in the spatial domain. Next, in order to weaken the interference of phase unwrapping errors and other undesired phase contributions, an additional correction procedure is implemented 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.

Corrections to “InSAR Phase Unwrapping Error Correction for Rapid Repeat Measurements of Water Level Change in Wetlands”

In the above article <xref ref-type="bibr" rid="ref1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[1]</xref> , Table I(b) cited an incorrect reference number. Reference [12] should have been given as [13], provided here as <xref ref-type="bibr" rid="ref2" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[2]</xref> .

Go Extra Miles: An Additional Error Correction Procedure Aimed to Further Improve Phase Unwrapping Accuracy and Reduce Creep Model Uncertainty

AbstractInterferometric Synthetic Aperture Radar (InSAR) phase unwrapping error is a major limiting factor on the InSAR‐derived tectonic deformation velocity. This is particularly the case when atmospheric turbulence, large deformation gradient and strong phase noise exist. To address limitations of existing phase unwrapping error correction methods, here we present a new algorithm that integrates decorrelation phase correction, triplet phase closure (TPC) test and integer linear programming (ILP) to overcome this limit. The rationale behind is that we mitigate the phase inconsistency using decorrelation correction and then detect the phase unwrapping error magnitude using TPC. Next we borrow the ILP from Compressed Sensing that converts the phase unwrapping error correction to a sparse signal recovery problem. We demonstrated the validity of our method by using synthetic data and 5‐year Sentinel‐1 real data covering the Central San Andreas Fault creeping section, where exists obvious tectonic deformation, strong atmospheric disturbance and decorrelated scatterers, and the inverted long‐term creep model constrained by InSAR velocity after correction shows a lower uncertainty than that constrained by the uncorrected one.

Kotrupi landslide deformation study in non-urban area using DInSAR and MTInSAR techniques on Sentinel-1 SAR data

The DInSAR (Differential Interferometric SAR) and MTInSAR (Multi-Temporal Interferometric SAR) techniques are used to examine a surface displacement in the Kotrupi Region in this paper. DInSAR and MTInSAR are capable of determining the surface deformation of a rapidly moving landslide. The Vertical Line of Sight (LOS) displacements were estimated with millimeter accuracy using a DInSAR technique followed by phase unwrapping. MTInSAR approaches using APS (Atmospheric Phase Screen) and sparse point processing, on the other hand, measure earth surface displacements and track their trends over time. DInSAR is limited by several difficulties, including phase decorrelation errors, phase unwrapping errors, and atmospheric phase disturbances, all of which reduce the quality of deformation effects. MTInSAR approaches, on the other hand, use data from several different periods within the same temporal baseline. As a result, the effect atmospheric phase disturbances and unwrapping error is greatly decreased when compared to classic DInSAR approaches. After the Kotrupi landslide of August 13, 2017, conventional DInSAR with a single pair of SLC (Single Look Complex) Sentinel-1 SAR images showed a maximum displacement value of about −60 mm to 60 mm in the Kotrupi landslide runoff region. While the advanced MTInSAR results indicate a maximum rate of velocity of about −45 mm/year for the continuous deformation happening in the Kotrupi landslide area. The coherence values along Pathankot National Highway (NH) −154 before and after the landslide were 0.857 and 0.019, respectively. Deformation studies before and after the landslide occurrence are also conducted using a DEM (Digital Elevation Model). Based on the DEM obtained, erosional and depositional deformations of −3.5 m and +3.0 m have been recorded in the Kotrupi landslide runoff area, resulting in 6–7 m change and material loss. The Root Mean Square Error (RMSE) for MTInSAR DEM 0.787 m and DInSAR DEM 1.026 m was estimated after the DEMs produced from DInSAR and MTInSAR processing were compared with TanDEM-X. MTInSAR produces much better results than DInSAR in non-urban areas.

Comparison of Phase Estimation Methods for Quantitative Susceptibility Mapping Using a Rotating-Tube Phantom.

Quantitative Susceptibility Mapping (QSM) is an MRI tool with the potential to reveal pathological changes from magnetic susceptibility measurements. Before phase data can be used to recover susceptibility (Δχ), the QSM process begins with two steps: data acquisition and phase estimation. We assess the performance of these steps, when applied without user intervention, on several variations of a phantom imaging task. We used a rotating-tube phantom with five tubes ranging from Δχ=0.05 ppm to Δχ=0.336 ppm. MRI data was acquired at nine angles of rotation for four different pulse sequences. The images were processed by 10 phase estimation algorithms including Laplacian, region-growing, branch-cut, temporal unwrapping, and maximum-likelihood methods, resulting in approximately 90 different combinations of data acquisition and phase estimation methods. We analyzed errors between measured and expected phases using the probability mass function and Cumulative Distribution Function. Repeatable acquisition and estimation methods were identified based on the probability of relative phase errors. For single-echo GRE and segmented EPI sequences, a region-growing method was most reliable with Pr (relative error <0.1) = 0.95 and 0.90, respectively. For multiecho sequences, a maximum-likelihood method was most reliable with Pr (relative error <0.1) = 0.97. The most repeatable multiecho methods outperformed the most repeatable single-echo methods. We found a wide range of repeatability and reproducibility for off-the-shelf MRI acquisition and phase estimation approaches, and this variability may prevent the techniques from being widely integrated in clinical workflows. The error was dominated in many cases by spatially discontinuous phase unwrapping errors. Any postprocessing applied on erroneous phase estimates, such as QSM's background field removal and dipole inversion, would suffer from error propagation. Our paradigm identifies methods that yield consistent and accurate phase estimates that would ultimately yield consistent and accurate Δχ estimates.