Unwrapping Errors Research Articles

Deciphering Small-Scale Seasonal Surface Dynamics of Rock Glaciers in the Central European Alps Using DInSAR Time Series

The Essential Climate Variable (ECV) Permafrost is currently undergoing strong changes due to rising ground and air temperatures. Surface movement, forming characteristic landforms such as rock glaciers, is one key indicator for mountain permafrost. Monitoring this movement can indicate ongoing changes in permafrost; therefore, rock glacier velocity (RGV) has recently been added as an ECV product. Despite the increased understanding of rock glacier dynamics in recent years, most observations are either limited in terms of the spatial coverage or temporal resolution. According to recent studies, Sentinel-1 (C-band) Differential SAR Interferometry (DInSAR) has potential for monitoring RGVs at high spatial and temporal resolutions. However, the suitability of DInSAR for the detection of heterogeneous small-scale spatial patterns of rock glacier velocities was never at the center of these studies. We address this shortcoming by generating and analyzing Sentinel-1 DInSAR time series over five years to detect small-scale displacement patterns of five high alpine permafrost environments located in the Central European Alps on a weekly basis at a range of a few millimeters. Our approach is based on a semi-automated procedure using open-source programs (SNAP, pyrate) and provides East-West displacement and elevation change with a ground sampling distance of 5 m. Comparison with annual movement derived from orthophotos and unpiloted aerial vehicle (UAV) data shows that DInSAR covers about one third of the total movement, which represents the proportion of the year suited for DInSAR, and shows good spatial agreement (Pearson R: 0.42–0.74, RMSE: 4.7–11.6 cm/a) except for areas with phase unwrapping errors. Moreover, the DInSAR time series unveils spatio-temporal variations and distinct seasonal movement dynamics related to different drivers and processes as well as internal structures. Combining our approach with in situ observations could help to achieve a more holistic understanding of rock glacier dynamics and to assess the future evolution of permafrost under changing climatic conditions.

Phase correction based SNR enhancement for distributed acoustic sensing with strong environmental background interference

Fiber-optic distributed acoustic sensing (DAS) systems based on phase-sensitive optical time domain reflectometry (Φ-OTDR) measure acoustic waves by demodulating the phase variations of the Rayleigh backscattering (RBS) signals in a sensing optical fiber. However, in harsh environments, strong environmental background interference, coupled with the interference fading of the RBS, would introduce severe distortions in DAS signal that cannot be corrected or even can be worsened by phase unwrapping, thus resulting in low signal to noise ratio (SNR) and even undetectable signal. In this work, a novel method based on trend prediction is proposed to correct the distortions induced by phase unwrapping error around the fading points. The method is further validated in processing the data acquired from a field test performed in ocean environments using a home-built DAS system. By locating and erasing the distortion points, and then detrending, the acoustic signal buried in strong environmental background interference is retrieved with an SNR improvement greater than 10 dB. The results show that the proposed phase correction method can effectively enhance DAS's SNR for those challenging applications with strong background interference.

Phase Unwrapping Error Correction Based on Multiple Linear Regression Analysis

Fringe projection profilometry (FPP) is prone to phase unwrapping error (PUE) due to phase noise and measurement conditions. Most of the existing PUE-correction methods detect and correct PUE on a pixel-by-pixel or partitioned block basis and do not make full use of the correlation of all information in the unwrapped phase map. In this study, a new method for detecting and correcting PUE is proposed. First, according to the low rank of the unwrapped phase map, multiple linear regression analysis is used to obtain the regression plane of the unwrapped phase, and thick PUE positions are marked on the basis of the tolerance set according to the regression plane. Then, an improved median filter is used to mark random PUE positions and finally correct marked PUE. Experimental results show that the proposed method is effective and robust. In addition, this method is progressive in the treatment of highly abrupt or discontinuous regions.

Phase-sensitive optical time domain reflectometry based on geometric phase measurement

A phase-sensitive optical time domain reflectometer based on coherent heterodyne detection of geometric phase in the beat signal of light, is reported for the first time to our knowledge. The use of the geometric phase to extract strain makes it immune to polarisation diversity fading. This is because a polarisation mismatch between the interfering beams is not a hindrance to its measurement. The geometric phase is calculated using the amplitude of the beat signal and individual beam intensities without any need for phase unwrapping. It is measured per beat period and can be equated with the traditionally measured dynamic phase with appropriate scaling. The results show that the system based on the geometric phase successfully measures strain, free from polarisation mismatch fading and phase unwrapping errors, providing a completely novel solution to these problems.

Slow‐Moving Landslides Triggered by the 2016 Mw 7.8 Kaikōura Earthquake, New Zealand: A New InSAR Phase‐Gradient Based Time‐Series Approach

AbstractEarthquake‐triggered slow‐moving landslides are not well studied mainly due to a lack of high‐resolution in‐situ geodetic observations both in time and space. Satellite‐based interferometric synthetic aperture radar (InSAR) has shown potential in landslides applications, however, it is challenging to detect earthquake‐triggered slow‐moving landslides over large areas due to the effects of post‐seismic tectonic deformations, atmospheric delays, and other spatially propagated errors (e.g., unwrapped errors caused by decorrelation noises). Here, we present a novel InSAR phase‐gradient‐based time‐series approach to detect slow‐moving landslides that triggered by the 2016 Mw 7.8 Kaikōura earthquake. Twenty‐one earthquake‐triggered large (>0.1 km2) slow‐moving landslides are detected and studied. Our results reveal decaying characteristics of the temporal evolutions of these landslides, that averagely 3.9 years after the earthquake, their post‐seismic velocity will decay by 90% to reach approximately the pre‐seismic level. Our study opens new perspectives for understanding mass balance of earthquakes and helps reduce associated hazards.

Time series phase unwrapping algorithm using LP-norm optimization compressive sensing

Time series phase unwrapping is an essential step in the time series interferometric synthetic aperture radar technique for deformation monitoring. However, traditional unwrapping algorithms are prone to unwrapping errors in the case of intense noise and steep deformation gradients, which directly affect the accuracy of the deformation information interpretation. To address this problem, a time series phase unwrapping algorithm using LP-norm optimization compressive sensing is proposed in this paper. This algorithm first transforms the minimizing L0-norm describing compressive sensing technique into a nonconvex problem with weaker constraints, that is, minimizing the LP-norm. Then, an optimized compressed sensing model was proposed by combining the constraint criterion of the phase triplet closure in the temporal domain and the solution strategy of the iterative reweighted least squares method. Improved temporal dimensional phase unwrapping and unwrapping error correction algorithms were developed based on this optimized model. Finally, the proposed algorithm was perfected by combining the above improved methods and the pseudo-three-dimensional phase unwrapping framework. Simulated and Sentinel-1A real datasets verify that the proposed algorithm has better noise robustness, unwrapping stability, and efficiency than traditional algorithms, particularly in the case of a steep deformation gradient and intense noise. The temporal coherence estimated by the proposed algorithm for the real dataset is generally greater than 0.99, which is far superior to traditional algorithms. Furthermore, the proposed algorithm facilitates high-precision interpretation of deformation information. The cross-validation results show that the deformation results obtained by traditional algorithms are underestimated by at least 73 mm/a and 68 mm at the maximum subsidence than the DSInSAR. However, the deformation result obtained by the proposed algorithm is highly consistent with that of the DSInSAR.

Selection of optimal frequencies in multiple-frequency fringe projection profilometry

The selection of frequencies which are in some sense optimal is an open research problem in phase shifting profilometry. We propose a novel method for selecting multiple frequencies for phase shifting profilometry. The frequencies are selected to provide the best possible resistance to phase unwrapping errors when temporal unwrapping is used. The proposed frequency selection method is based on the maximization of the minimal distance between lines of the line-constellation in the wrapped phase space. It is realized as an exhaustive search over the fringe counts, which is more efficient than searching over the frequencies or over the wavelengths. We also propose an efficient and effective method for filtering points for which the phase may be incorrectly unwrapped. The proposed filtering method is based on limiting the distance between the wrapped phase measurement and the line of the line-constellation. We demonstrate the applicability of the proposed frequency selection method through the construction and the experimental validation of several frequency designs which contain only high frequencies, and which are insensitive to large errors in wrapped phase. We also demonstrate the effectiveness of the proposed filtering.

Simulated wrapped phase optimizes phase retrieval in phase-shifting interferometry.

Phase retrieval is crucial in phase-shifting interferometry and other phase measurement techniques. However, in noisy wrapped phase maps with high steepness, discontinuities arise and cause phase unwrapping errors. To solve this problem, this Letter presents a phase retrieval method based on a simulated wrapped phase. By establishing the correspondence between the simulated and measured interferograms, the difference in wrapped phases between them can be obtained. The difference in wrapped phase map, which has sparse and wide interference fringes, has a higher reliability of phase unwrapping. The proposed method not only possesses high phase retrieval accuracy but it also simplifies the processing of interferograms. Furthermore, the layout of all interferometric systems, the parameters of optical components, and the model of the measured object are known, so the proposed method can be used as a reference for phase retrieval.

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.

Half-Period Gray-Level Coding Strategy for Absolute Phase Retrieval

N-ary gray-level (nGL) coding strategy is an effective method for absolute phase retrieval in the fringe projection technique. However, the conventional nGL method contains many unwrapping errors at the boundaries of codewords. In addition, the number of codewords is limited in only one pattern. Consequently, this paper proposes a new gray-level coding method based on half-period coding, which can improve both these two deficiencies. Specifically, we embed every period with a 2-bit codeword, instead of a 1-bit codeword. Then, special correction and decoding methods are proposed to correct the codewords and calculate the fringe orders, respectively. The proposed method can generate n2 codewords with n gray levels in one pattern. Moreover, this method is insensitive to moderate image blurring. Various experiments demonstrate the robustness and effectiveness of the proposed strategy.

A model-backfeed deformation estimation method for revealing 20-year surface dynamics of the Groningen gas field using multi-platform SAR imagery

• The model-backfeed deformation estimation method offers more reliable InSAR deformation parameter estimations. • Multiple Hypothesis Testing is employed to determine the best deformation models. • Geolocation error ellipsoids and Monte Carlo methods are used for spatial integration. • Three SAR missions are used to map 20-year Groningen gas field subsidence. The Groningen gas field, the largest natural gas field in Europe, was discovered in 1959 and started its production in 1963. The Earth surface above it experienced subsidence over the past six decades because of gas extraction activities. To accurately reveal this surface movement with satellite SAR data, our study first proposes and demonstrates a model-backfeed (MBF) InSAR deformation estimation method to improve InSAR deformation time series modeling. This method allowed us to include a priori knowledge and to iteratively optimize functional and stochastic models. Using this method and employing a spatio-temporal SAR data integration method based upon Monte Carlo and Multiple Hypothesis Testing methods, we retrieved the 20-year subsidence history of the Groningen gas field by integrating 32 ERS-1/2, 68 Envisat and 82 Radarsat-2 SAR images. The results show that the maximum cumulative surface subsidence in this gas field has been as much as 15.5 cm between 1995 and 2015. In terms of precision and accuracy, our MBF method offered a better result than the standard Multi-Temporal InSAR analysis method: the Ensemble Coherence increased by 10%–19% and Spatio-Temporal Consistency decreased by 2%–20%. In terms of accuracy, our results better concur with the external GNSS reference observations. We further show that the spatio-temporal SAR data integration method has better links with multi-platform SAR data if the uncertainties of the InSAR geolocation and temporal deformation are included. The study demonstrates that the MBF method optimized the estimation of deformation parameters and mitigated unwrapping errors.

Error analysis and 3D reconstruction using airborne array InSAR images

Multi-temporal synthetic aperture radar interferometry (MT-InSAR) is able to detect surface deformation and reconstruct a 3D surface model with high precision but requires a long observation period to accumulate the multi-baseline SAR images. The airborne array InSAR system is able to acquire a stack of multi-baseline SAR images in a single acquisition, which significantly improves the 3D modeling capability. However, processing the images obtained by the low-altitude platform using the conventional model will lead to geometric approximation (GA) errors, such as flattened phase error and reference error, which degrade the precision of the 3D reconstruction. In this paper, we quantitatively analyze the error sources of the array-InSAR interferograms and design a hybrid 3D phase unwrapping approach for 3D reconstruction. A hypothesis test is developed to identify the phase ambiguity by comparing the initial solution of the least-square with that of the beam-forming. Three indicators are proposed to identify the reliable arcs, achieving a reliable phase unwrapping. The L1 norm approach is adopted to detect the unwrapping errors during the spatial unwrapping and a two-tie network strategy is used to process the data in the individual blocks from the perspective of global optimization. Furthermore, an iterative scheme is recommended to compensate the geometric approximation errors. The main advantage of the proposed algorithm is the compensation of the GA error and reliable phase unwrapping. The experimental results by both simulated and real SAR data show that the proposed algorithm can eliminate the GA error and provide a viable solution to rapid 3D SAR imaging with an airborne platform.

COMPARISON AND EVALUATION OF DIFFERENT APPROACHES FOR EFFICIENT PROCESSING OF LONG GROUND-BASED SAR TIMES SERIES

Abstract. Ground-based Synthetic Aperture Radar (GB-SAR) is a monitoring tool which, once installed, acquires a large amount of data autonomously. For the IBIS-FM system, approximately 760 SAR images per day are acquired, which corresponds to more than 23 000 scenes per month. Therefore, this paper analysis different strategies for the interferometric processing of such large data stacks to find a compromise between accuracy, computational effort and the ability to (re-)process specific time intervals independently. This study compares the single master approach with the sequential approach and in addition two block-wise approaches. Moreover, a new baseline configuration called Daily Baseline Subset (DBAS) is compared which uses interferograms having a multiple of one day as temporal baseline. We evaluate them on a data stack of 30 000 images, acquired at Enguri Dam in Georgia. We check the unwrapping errors and the quality of the displacement estimation to compare the different configurations. We found that block-wise approaches show the best results considering unwrapping errors and Root Mean Square Error, while in our study the DBAS approach shows to the most plausible displacement map which is also dependent on the individual reduction of atmospheric noise.

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.