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Multitemporal synthetic aperture radar interferometry (MT-InSAR) is able to reconstruct a 3-D surface model with high precision but requires a long waiting time to get the multibaseline synthetic aperture radar (SAR) images. The array InSAR system can acquire multibaseline images in a single flight, which significantly improves the practical capability of 3-D reconstruction. However, the array InSAR system with many channels has very high complexity in both system and processing because of cross-channel calibration and decoupling. Thus, reducing the number of channels requires the investigation of the 3-D reconstruction algorithm to be suitable for sparse array InSAR images. This work proposed an asymptotic 3-D phase unwrapping (PU) algorithm for 3-D reconstruction using sparse array InSAR images, i.e., as few as three or four channels. A 2-D (space) + 1-D (baseline) PU framework is developed to improve the reliability of the 3-D PU, and a novel asymptotic strategy is proposed for the combination of the short–long baseline interferogram. Using successful unwrapping (SU) criteria, the bounds of the possible baseline combinations and the expected minimal coherence are derived, respectively. The main advantage of the proposed algorithm is the reliable PU with very sparse channels and an analysis of the possible baseline combinations. The experimental results by both the simulated and real data show that the proposed method can achieve a 3-D reconstruction using only three-pass array InSAR images and optimize the baseline design for the array InSAR system. [ABSTRACT FROM AUTHOR]

Two-dimensional phase unwrapping (PU) is a classical ill-posed problem in synthetic aperture radar interferometry (InSAR). The traditional algorithmic model-based 2-D PU methods are limited by the Itoh condition, which is from the PU researchers’ experience and has critical challenges under strong phase noises or violent phase changes. Recently, advanced learning-based 2-D PU methods could break through the limitation of the Itoh condition owing to their data-driven frameworks, offering promising results in terms of both the speed and accuracy. The one-step learning-based PU method, as one of the representatives, retrieves the unwrapped phase directly from the wrapped phase through regression. However, the main disadvantage of one-step learning-based PU is that it usually blurs the output unwrapped phase due to its $L_{2}$ loss, that is, it cannot guarantee the congruency between the rewrapped interferometric fringes of the PU solution and the input interferogram. To solve this problem, we propose a one-step 2-D PU method based on the conditional generative adversarial network (referred to as PU-GAN), which treats 2-D PU as an image-to-image translation problem. The generator in PU-GAN can be trained to generate the unwrapped phase through minimizing a $L_{1}$ -norm loss based on a U-Net architecture, while simultaneously the corresponding discriminator can learn an adversarial loss by a structure of Patch-GAN that tries to classify if the output unwrapped phase image is real or fake. Both a theoretical analysis and the experimental results show that the proposed method outperforms the representative algorithmic model-based and learning-based 2-D PU methods. [ABSTRACT FROM AUTHOR]

Multibaseline (MB) phase unwrapping (PU) is a critical processing step for the MB synthetic aperture radar interferometry (InSAR). Compared with the traditional single-baseline (SB) PU, MB PU has wider application scope on the study area with strong phase variation, because it can overcome the limitation of the Itoh condition. Since most of the MB PU methods need to process multiple interferograms simultaneously, the size of the input interferograms will pose unique challenges when it exceeds the limit of computational capabilities. Until now, the research achievements related to large-scale (LS) MB PU have been quite limited. To deal with such case, we propose a technique for applying the two-stage programming-based MB PU method (TSPA) proposed by Yu and Lan to the LS MB InSAR data set in this paper. To be specific, the MB $L^\kappa $ -norm envelope-sparsity theorem is proposed and proved first, which gives a sufficient condition to exactly guarantee the consistency between local and global TSPA solutions. Afterward, based on the MB $L^\kappa $ -norm envelope-sparsity theorem, we put forward an interferogram tiling strategy, whereby each LS interferogram in the input MB InSAR data set is partitioned into a set of several smaller sub-interferograms that can be unwrapped individually by TSPA in parallel or in series. Both theoretical analysis and experimental results show that the proposed tiling strategy is effective for the LS MB PU problem. [ABSTRACT FROM AUTHOR]

Multibaseline (MB) synthetic aperture radar interferometry (InSAR) has the potential to improve the traditional single-baseline InSAR from the ill-posed problem to the well-posed problem. It is because MB InSAR phase unwrapping (PU) can take advantage of the baseline diversity to significantly increase the ambiguity intervals of interferometric phases, so it completely overcomes the limitation of the phase continuity assumption. However, due to the mathematical foundation of most of the MB PU methods, i.e., the Chinese remainder theorem (CRT), has poor measurement bias robustness (measurement bias could be caused by surface deformation, atmospheric artifact, and phase noise), CRT is sensitive to the normal baseline length. In other words, even if we choose the same CRT-based MB PU method, different system baseline lengths could result in different PU performances. Therefore, how to choose the baseline lengths to optimize CRT performance is crucial to all the CRT-based MB PU methods. In this paper, a nonlinear mixed-integer programming-based baseline design criterion (referred to NIP criterion) is proposed to maximize the measurement bias tolerance of the CRT-based MB PU. The optimality condition of the NIP criterion quantitatively provides important instructions for the CRT-based MB PU applications and offers significant guidance in the development of the practical MB InSAR system. The experiment results are shown to verify the effectiveness of the NIP criterion by using three representative CRT-based MB PU methods. [ABSTRACT FROM AUTHOR]

The reliability of persistent scatterer interferometry (PSI) is directly related to the accurate phase unwrapping (PU) of the 3-D (2-D space and time) sparse data stack. Phase ambiguities estimated using temporal phase unwrapping (TPU) are crucially exploited in most 3-D PU algorithms. However, most TPU methods are not noise-robust owing to the independent processing of each arc in the persistent scatterer network. To solve this problem, the cluster-analysis-based PU method for digital elevation model (DEM) construction is adapted to the phase ambiguity estimation problem for PSI in this letter. First, for each arc, the interior relation among phase ambiguities in multiple interferograms is derived to be linear and can be represented by an intercept vector. Subsequently, arcs with the same ambiguities are clustered according to their intercept vectors because arcs with identical phase ambiguities are verified to have the same intercept vectors. Moreover, a more reliable intercept vector can be calculated for each arc cluster by combining the intercept vectors within the cluster. Finally, more precise phase differences are estimated for each cluster using the corresponding intercept vector so that all the arcs are better unwrapped. Both the simulated and real experiments indicate the effectiveness and superiority of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The three-pass differential synthetic aperture radar interferometry (DInSAR) is one of the approaches in radar interferometry applications for measuring the deformation of the earth surface. The conventional three-pass DInSAR needs a successful single-baseline (SB) phase unwrapping (PU) procedure on each interferogram to ensure accurate deformation monitoring. Because of the limitation of the phase continuity assumption, the SB PU becomes a challenging processing step when the study area has strong phase variation. In this paper, the multibaseline (MB) InSAR PU methodology, which can eliminate the phase continuity assumption by means of the baseline diversity, is transplanted into the conventional three-pass DInSAR domain. Based on MB PU, a novel terrain deformation estimation approach is developed. Both theoretical analysis and experimental results demonstrate that the proposed method is an effective surface deformation estimation method. [ABSTRACT FROM AUTHOR]

For airborne repeat-pass synthetic aperture radar interferometry (InSAR), precise trajectory information is needed to compensate for deviations of the platform movement from a linear track. Using the trajectory information, motion compensation (MoCo) can be implemented within SAR data focusing. Due to the inaccuracy of current navigation systems, residual motion errors (RMEs) exist between the real and measured trajectory, causing phase undulations in the final interferograms. Up to now, MoCo and RME estimation have usually been combined in airborne InSAR to estimate ground deformation. Conventional MoCo methods generally involve azimuthal and range resampling and phase correction. Then frequency-domain focusing techniques can be used to generate the SAR images. After focusing SAR images with MoCo, both multisquint and autofocus approaches can be used to estimate RME. In addition to the MoCo-based frequency-domain focusing, the time-domain backprojection (BP) technique can also focus the SAR data obtained from highly nonlinear platform trajectories. In this paper, we present, for the first time, the combination of BP and multisquint techniques for RME estimation. A detailed derivation of the implementation of the multisquint approach using the BP-focusing images is presented. Repeat-pass data from the SlimSAR system over Slumgullion landslide are used to demonstrate the feasibility of RME estimation for both stationary and nonstationary scenes. We conclude that the proposed method can effectively remove the RME. [ABSTRACT FROM AUTHOR]

Two-dimensional phase unwrapping (PU) is a crucial processing step of synthetic aperture radar interferometry (InSAR). With the rapid advance of InSAR technology, the scale of interferograms is becoming increasingly larger. When the size of the input interferogram exceeds computer hardware capabilities, PU becomes more problematic in terms of computational and memory requirements. In the case of “big-data” PU, the input interferogram needs to be first tiled into a number of subinterferograms, unwrapped separately, and then spliced together. Hence, whether the PU result of each subinterferogram is consistent with that of the whole interferogram is critical to the large-scale PU process. To effectively solve this problem, the L^1 -norm envelope-sparsity theorem, which gives a sufficient condition to exactly guarantee the consistency between local and global L^1 -norm PU solutions, is put forward and proved. Furthermore, the L^0 -norm envelope-sparsity theorem, which gives a sufficient condition to exactly guarantee the consistency between local and global L ^0 -norm PU solutions, is also proposed and proved. Afterward, based on these two theorems, two tiling strategies are put forward for the large-scale L^0 -norm and L^1 -norm PU methods. In addition, this paper presents the concepts of the tiling accuracy and the tiling resolution, which are the criteria used to evaluate the effectiveness of a tiling strategy, and we use them to quantitatively analyze the aforementioned tiling strategies. Both theoretical analysis and experimental results show that the proposed tiling strategies are effective for the large-scale L^0 -norm and L^1 -norm PU problems. [ABSTRACT FROM PUBLISHER]

Two-dimensional phase unwrapping (PU) is a critical processing procedure of synthetic aperture radar interferometry. Thus far, many PU methods with high accuracy have been proposed. However, the limitation of computer's memory requirement is ignored in the design of most of these methods. To effectively solve this problem, a fast PU method for large-scale interferograms is proposed in this paper. With this method, a large-scale interferogram is first partitioned into small tiles according to a strategy based on the residue clustering characteristics, which is the extension and improvement of our previous work. The new tiling strategy has a significant advantage over our earlier work, since it can exactly ensure the consistency between local and global PU results of the L^1-norm criterion. In order to solve the dilemma that high execution speed and high accuracy cannot be satisfied at the same time, which is usually encountered in practice, each tile will be independently unwrapped by minimum-spanning-tree-based PU method either in parallel or in series after tiling processing. By comparing between two representative large-scale PU methods (the SNAPHU method proposed by Chen and Zebker and a large-scale minimum-cost flow method supplied by GAMMA software), it can be seen that the proposed approach is not only efficient in solving large-scale PU problems but also effective in avoiding the inconsistency between local and global PU results generated by image tiling. [ABSTRACT FROM AUTHOR]

Multibaseline phase unwrapping is a critical processing procedure of multibaseline synthetic aperture radar interferometry (InSAR). It has an advantage over single-baseline phase unwrapping in discontinuous-terrain-height estimation. In this paper, the pixels' combination information of multiple InSAR interferograms with different baseline lengths is deeply investigated, and the term ambiguity vector is proposed to represent a pixel's ambiguity number of multiple interferograms. It is also revealed that pixels with the same ambiguity vector have an exclusive pattern among them. A fast cluster-analysis (CA)-based method is proposed for multibaseline phase unwrapping. In this method, all pixels are first clustered into different groups according to their patterns, and then, information of the cluster center is used to unwrap the phases of pixels group by group. Simulation results are shown to verify the effectiveness, efficiency, and noise robustness of CA multibaseline phase-unwrapping method. [ABSTRACT FROM AUTHOR]

The problem of phase unwrapping (PU) in synthetic aperture radar (SAR) interferometry (InSAR) is caused by the measured range differences being ambiguous with the wavelength. Therefore, multi-baseline (MB) is a key processing step of MB InSAR. Compared with the traditional single-baseline (SB) PU, MB PU is advantageous in solving steep terrain due to its ability to break through the constraint of the phase continuity assumption. However, the accuracy of most of the existing MB PU methods is still limited to its mathematical foundation, i.e., the Chinese remainder theorem (CRT) is too sensitive to measurement bias. To solve this issue, this paper presents a refined algorithm based on the two-stage programming MB PU approach (TSPA) proposed by H. Yu. The significant advantage of the refined TSPA method (abbreviated as LPM-TSPA) is that it improves the performance of stage 1 of TSPA through assuming terrain height surface in the neighborhood pixels can be approximated by a plane to combine more information of the interferometric phase in the local region to estimate the ambiguity number gradient. The experiment results indicate that the LPM-TSPA method can significantly improve the accuracy of the MB PU solution. [ABSTRACT FROM AUTHOR]