A Convex Hull and Cluster-Analysis Based Fast Large-Scale Phase Unwrapping Method for Multibaseline Sar Interferograms

Phase unwrapping (PU) is a key processing step in interferometric synthetic aperture radar (InSAR). To date, a number of skillful single-baseline (SB) and multibaseline (MB) PU methods exhibiting different advantages have been proposed. However, as the basic principles of SB and MB PUs are essentially different, it is difficult to effectively and systematically compare the performance of SB and MB PUs, despite the knowledge that this type of analysis is important for allowing the ever-increasing number of InSAR practitioners to choose a suitable approach for practical applications and to optimally plan future InSAR satellite missions. Recently, the framework of the two-stage programming approach (TSPA) was proposed, and this allows for the majority of the existing SB PU methods to be transplanted into the MB domain, to allow practitioners to feasibly and comprehensively compare SB and MB PU methodologies. In this study, the digital elevation model (DEM) reconstruction accuracy is compared between the classical SB PU methods and their corresponding TSPA-framework-based MB PU methods using the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L^{p}$ </tex-math></inline-formula> -norm model. Interestingly, we observed that although the number of PU residues in the MB case is larger than that in the SB case, the MB PU performance is better. The reason for this is that the type of MB residue is typically dipole, so the average length of the required MB branch-cut is shorter than that of SB. It is also demonstrated that the TSPA framework can effectively improve the PU accuracy of many existing SB PU methods when the number of input interferograms is sufficient.

Multibaseline (MB) synthetic aperture radar inter-ferometry (InSAR) is capable of reconstructing steep terrain height profiles, and MB phase unwrapping (PU) is one of the most critical and challenging steps in its processing chain. Existing MB PU algorithms usually suffer from poor noise robustness or low computational efficiency. In this work, we propose a fast and robust MB PU algorithm, including three main steps: 1) construct the triangulation network guided by the quality map; 2) obtain robust estimation of ambiguity number gradients based on the intrinsic relationship between interferograms and gradient regularization; 3) solve minimum cost flow problem with modified weights. The mean absolute errors of the height profiles constructed by the proposed method are 1.6m and 1.3m for simulated data and real data experiments respectively, verifying the effectiveness of the proposed method.

For synthetic aperture radar (SAR) interferometry (InSAR), phase unwrapping (PU) is an important and difficult step. Due to the high computational complexities of the classical and skilled PU methods, the size and number of interferograms to be processed together must be considered in InSAR applications. However, with the rapid development of InSAR technology, the scale of interferometric data has significantly increased, which has brought two difficulties to InSAR processing: 1) excessive memory consumption and 2) unacceptably long computing time. To solve these problems, a fast large-scale PU method based on cluster analysis and convex hull (CCFLS) is proposed in this paper. It was developed for single-baseline (SB) InSAR and refined under the multibaseline (MB) two-stage programming approach InSAR (TSPA-InSAR) framework. The main idea of CCFLS is to reduce the consumption of computing resources by discarding the PU processing of worthless low quality areas. The key to this work is to determine the discarded region at a low computational cost while ensuring the same PU accuracy for the remaining region as global processing. The theoretical analysis demonstrates the advantage of the CCFLS method for large-scale InSAR data processing, and experiments also verify that CCFLS can greatly reduce the consumption of computing resources while ensuring the PU accuracy of the solved region.

Multibaseline (MB) synthetic aperture radar (SAR) tomography is a promising mode of SAR interferometry, allowing full 3-D imaging of volumetric and layover scatterers in place of a single elevation estimation capability for each SAR cell However, Fourier-based MB SAR tomography is generally affected by unsatisfactory imaging quality due to a typically low number of baselines with irregular distribution. In this paper, we improve the basic elevation focusing technique by reconstructing a set of uniform baselines data exploiting in the interpolation step the ancillary information about the extension of a height sector which contains all the scatterers. This <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">priori</i> information can be derived from the knowledge of the kind of the observed scenario (e.g., forest or urban). To demonstrate the concept, an imaging enhancement analysis is carried out by simulation.

Phase unwrapping (PU) has been a key step in the processing of interferometric synthetic aperture radar (InSAR) data, and its processing accuracy will directly affect the reconstruction results of digital elevation models (DEMs). The traditional single-baseline (SB) PU must be calculated under continuity assumptions. However, multi-baseline (MB) PU can get rid of the limitation of continuity assumption, so reasonable results can be obtained in regions with large gradient changes. However, the poor noise robustness of MBPU has always been a key problem. To address this issue, we transplant three Bayesian filtering methods with a two-stage programming approach (TSPA), and propose corresponding MBPU models. First, we propose a gradient-estimation method based on the first step of TSPA, and then the corresponding PU model is determined according to different Bayesian filtering. Finally, the wrapped phase can be obtained by unwrapping, one by one, using an effective quality map based on heapsort. These methods can improve the robustness of the MBPU methods. More significantly, this paper establishes a novel TSPA-based Bayesian filtering MBPU framework for the first time. This is of great significance for broadening the research of MBPU. The proposed methods experiments on simulated and real MB InSAR datasets. From the results, we can see that the TSPA-based Bayesian filtering MBPU framework can significantly improve the robustness of the MBPU method.

The 3-D structure of forests is an important indicator for evaluating forest health and can provide data support for ecological monitoring and protection. Synthetic aperture radar (SAR) tomography (TomoSAR) is an important technology for forest structure estimation using the multibaseline (MB) SAR data stacks. The spectral estimators, such as the Capon method, are usually used to estimate the 3-D reflectivity along elevation direction. In this letter, a modified Capon (M-Capon) method is proposed to improve the estimated profiles of ground and canopy scatterers in the elevation direction, including the estimation accuracy and resolution. This method combines the ideas of the CLEAN algorithm with the Capon method and uses iteration to improve the resolution and accuracy of the estimation. The effectiveness of the M-Capon method is demonstrated using the simulated data and the MB SAR data acquired by the P-band airborne SAR system over the Saihanba Forest Farm in Hebei, China.

Multibaseline (MB) phase unwrapping (PU) is a key processing technique in MB interferometric synthetic aperture radar (InSAR). As one of the most popular methods, the cluster analysis (CA)-based MBPU method often suffers from the problem of low noise robustness. Therefore, the block-matching and 3D filtering (BM3D) algorithm, one of the most effective filtering methods for image denoising, is applied to improve the performance of the method. Five different filtering strategies for applying BM3D are proposed in the paper: interferogram filtering (IFF), intercept filtering (ICF), cluster number filtering (CNF), unwrapped phase filtering (UPF), and simultaneous filtering (STF). In particular, while keeping the general structure of BM3D, four different similarity measures are defined for interferograms, intercepts, clusters, and unwrapped phases to accommodate the special characteristics of different filtering objects. Experiments on synthesized and real InSAR datasets prove their feasibility and effectiveness, and the experiment results show that (1) the PU accuracy and robustness of the CA-based MBPU method can be greatly improved by adding BM3D denoising; (2) simultaneous filtering of interferograms, intercepts, cluster numbers, and unwrapped phases works best, but with the worst time complexity; (3) when filtering is performed for only one object of the CA-based MBPU method, the filtering effect of CNF and UPF is better than that of IFF and ICF; and (4), considering the three indicators of PUSR, NRSE, and time consumption, CNF and UPF should be the best choices.

This paper introduces new polarimetric algorithms for generating 3-D images and estimating scattering mechanisms from polarimetric multibaseline (MB) interferometric synthetic aperture radar (SAR) measurements. First, an MB interferometric SAR signal model is generalized to the fully polarimetric configuration, establishing the notion of polarimetric reflectivity. Subsequently, polarimetric beamforming, Capon, and MUSIC methods that determine optimal polarization combinations for height estimation are developed. These new techniques allow for extracting the height of reflectors, the associated scattering mechanisms, and the polarimetric (pseudo)reflectivities. By means of polarimetric dual-baseline interferometric SAR observations of an urban environment, the performance of the conceived algorithms is examined in detail. Producing 3-D images of a building layover, the quality of the approaches is compared in terms of refined resolution and lowered side lobes. Furthermore, the scattering processes occurring in urban scenes are investigated thoroughly by analyzing the optimal reflection types. The algorithms are validated using dual-baseline polarimetric SAR interferometric data at L-band acquired by German Aerospace Center's experimental SAR system over Dresden city.

Distributed spaceborne interferometric synthetic aperture radar (DS-InSAR) system includes more than one baseline, so it is also called multi-baseline InSAR system. It offers additional observation information for the derivation of position and height of object, compared to the single-baseline InSAR system. Based on the additional information it offers, a new DEM reconstruction approach of multi-baseline InSAR system is proposed. At first, theory of the approach is introduced and DEM reconstruction equations are derived. Then, error sensitivity analysis is made by first order approximation of Taylor expanding, which is validated by Monte-Carlo simulation. The results show that theoretical error analysis formula can give support for analysis and design of the system directly and the DEM accuracy is very sensitive to the interferometric phase difference error.

GaoFen-3 (GF-3) is the first fully polarimetric C-band synthetic aperture radar (SAR) satellite in China. Interferometric observation is an important capability of GF-3. However, the long temporal baseline is a great challenge for repeat-pass interferometric synthetic aperture radar (InSAR) processing, especially over mountainous areas. Phase noise and complex topography make phase unwrapping difficult. This paper proposes a step-wise approach for high-resolution InSAR data processing focusing on facilitating phase unwrapping. First, the coarse GF-3 digital elevation model (DEM) is reconstructed by InSAR processing with multilooking of large looks, which is used to suppress phase noise. Second, the coarse GF-3 DEM is used to remove the terrain phase from the InSAR phase with multilooking of small looks, which can reduce phase gradient and improve the accuracy of phase unwrapping. After several iterations, the GF-3 DEM is finally inversed with multilooking of 2 looks, which is of high resolution and high accuracy. The performance of GF-3 C-band InSAR data on the extraction of DEM is examined over a deciduous forested area with the proposed method. The root-mean-square error of the extracted GF-3 DEM is 3.78 m in comparison with the LiDAR DEM.

We investigated the Bayesian inferences using the maximize a posteriori (MAP) estimation for the problem of phase unwrapping in remote sensing using the synthetic aperture radar (SAR) interferometry. Then, in order to clarify performance of the Bayesian inference estimate, we carried out Monte Carlo simulation for a set of wave-fronts generated by an assumed true prior. Then, we clarified that optimal performance was achieved under the Bayes-optimal condition within statistical uncertainty. Then, we clarified that the present method was effective even for an artificial wave-front in remote sensing due to SAR interferometry. Also, we found that the Bayesian inference via the conjugate gradient method to derive the MAP solution for this problem. Using the numerical simulation for the wave-front, we found that the MAP estimation using the conjugate gradient method was effective for phase unwrapping as well as the MPM estimate approximately.

This paper explains the underestimation of phase slope and the consequent distortion of the phase surface, observed in two-dimensional (2-D) phase unwrapping by linear estimators, like least squares methods applied to synthetic aperture radar (SAR) interferometry. These methods minimize the difference between the gradient of the unwrapped phase and the wrapped differences of the measured wrapped phase. Using the probability distributions of phase noise and phase differences for a given coherence, the probability of a phase gradient error giving rise to a nonconservative vector field is derived. It is shown that this phase gradient error has nonzero mean in the presence of phase slopes. Linear phase estimators cannot distinguish the mean phase gradient error from a true phase slope; hence, the unwrapped phase shows a slope bias. This bias is quantified as a function of coherence and the number of independent samples that are averaged. The theoretical results are confirmed by simulations.

As is well known, multibaseline phase unwrapping (PU) is put forward to overcome single-baseline PU in discontinuous-terrain-height estimation. This letter presents a refined algorithm based on the cluster analysis (CA)-based noise-robust efficient multibaseline PU algorithm proposed by H. Yu. The basic idea is to combine multiple interferometric synthetic aperture radar interferograms with different baseline lengths by a linear combination. The new interferograms after the linear combination increase the ambiguity heights. The number of resulting groups on the envelope of the intercept histogram is decreased and the distance between different intercept groups is widened. Compared with the conventional CA method, the significant advantage of the refined CA (RCA) algorithm is that it improves noise robustness when the intercept groups are densely distributed. The proposed RCA algorithm is validated using the simulated interferometric data. The results demonstrate that the noise robustness performance is better than that of the CA method.

This paper presents the potential of differential synthetic aperture radar (SAR) interferometry to detect the gaps of the displacement rate between the buildings and the land surface. We assumed that the information about building surface displacement can be extracted from single look SAR images whereas the information about land surface deformation can be extracted from multi look SAR images. The proposed method implements Persistent Scatters (PS) InSAR and Small Baseline SAR (SBAS) techniques for respective purposes. Subtraction of the two results can detect the gaps. In addition, the proposed method corrects orbital phase error to mitigate phase ramp of the interferograms without phase unwrapping that is widely known to cause errors in applying to the areas where terrain is fluctuating. We applied the proposed method to Bangkok, Thailand, and found that it succeeded in detecting areas those have severe displacement rate gaps.

In this letter, two multi-baseline differential synthetic aperture radar (SAR) interferometry (DInSAR) techniques, high-coherent point (HCP) and interferometric point target analysis (IPTA), were applied to monitor the displacement of Lantau Highway as an example of a large-scale artificial linear feature (LALF), using 17 ENVISAT advanced synthetic aperture radar (ASAR) images. The phase ramp was exploited and removed, combining the merits of two different model coherence functions when sparse HCP candidates were encountered. Then, two velocity fields from the advanced DInSAR methods were compared and analysed. The results indicate that the improved HCP method could generate a smoother deformation trend than the IPTA approach at the expense of losing detail information.