Vision-Language-Action (VLA) models revolutionize robotic systems by enabling end-to-end perception-to-action pipelines that integrate multiple sensory modalities, such as visual signals processed by cameras and auditory signals captured by microphones. This multi-modality integration allows VLA models to interpret complex, real-world environments using diverse sensor data streams. Given the fact that VLA-based systems heavily rely on the sensory input, the security of VLA models against physical-world sensor attacks remains critically underexplored. To address this gap, we present the first systematic study of physical sensor attacks against VLAs, quantifying the influence of sensor attacks and investigating the defenses for VLA models. We introduce a novel ``Real-Sim-Real" framework that automatically simulates physics-based sensor attack vectors, including six attacks targeting cameras and two targeting microphones, and validates them on real robotic systems. Through large-scale evaluations across various VLA architectures and tasks under varying attack parameters, we demonstrate significant vulnerabilities, with susceptibility patterns that reveal critical dependencies on task types and model designs. We further develop an adversarial-training-based defense that enhances VLA robustness against out-of-distribution physical perturbations caused by sensor attacks while preserving model performance. Our findings expose an urgent need for standardized robustness benchmarks and mitigation strategies to secure VLA deployments in safety-critical environments.

Low-light vision remains a fundamental challenge in computer vision due to severe illumination degradation, which significantly affects the performance of downstream tasks such as detection and segmentation. While recent state-of-the-art methods have improved performance through invariant feature learning modules, they still fall short due to incomplete modeling of low-light conditions. Therefore, we revisit low-light image formation and extend the classical Lambertian model to better characterize low-light conditions. By shifting our analysis to the frequency domain, we theoretically prove that the frequency-domain channel ratio can be leveraged to extract illumination-invariant features via a structured filtering process. We then propose a novel and end-to-end trainable module named \textbf{F}requency-domain \textbf{R}adial \textbf{B}asis \textbf{Net}work (\textbf{FRBNet}), which integrates the frequency-domain channel ratio operation with a learnable frequency domain filter for the overall illumination-invariant feature enhancement. As a plug-and-play module, FRBNet can be integrated into existing networks for low-light downstream tasks without modifying loss functions. Extensive experiments across various downstream tasks demonstrate that FRBNet achieves superior performance, including +2.2 mAP for dark object detection and +2.9 mIoU for nighttime segmentation. Code is available at: \url{https://github.com/Sing-Forevet/FRBNet}.

Distributed scatterer interferometric synthetic aperture radar (DS InSAR) is a widely used technique for monitoring surface deformation, but its effectiveness is often compromised by temporal and spatial decorrelation, leading to degraded interferometric phase quality. Enhancing phase quality through phase linking (PL) is essential. However, existing PL methods struggle to produce high-quality sample coherence matrices (SCMs) due to the inhomogeneity and limited availability of low-coherence homogeneous samples. Consequently, accurately deriving phase matrices, sample coherence magnitude matrices (SCMMs), and precision matrices becomes challenging, significantly impacting the accuracy of PL estimation. To address these limitations, a two-step optimization-based PL (TSO-PL) method is proposed. TSO-PL integrates both the complex and real domain characteristics of the SCM and features two key innovations: 1) feature compression of the SCM (FC-SCM) to improve the signal-to-noise ratio of the phase and the accuracy of the coherence value in SCM and 2) adaptive nonlinear shrinkage of the SCMM (ANS-SCMM) to yield a more accurate SCMM by improving its structure. The simulation results demonstrate that TSO-PL is robust to variations in the estimation window size and homogeneous sample number, outperforming the phase triangulation algorithm (PTA), eigenvalue decomposition (EVD), and eigendecomposition-based maximum likelihood (EMI) methods in terms of accuracy and noise reduction. In a case study, TSO-PL improved the maximum deformation rate detection by 29.5%, 36.7%, and 31.1% compared with PTA, EVD, and EMI, respectively, with a significantly lower root mean square error (RMSE) of 11.3 mm. These findings demonstrate that TSO-PL effectively reduces phase noise, preserves fringe integrity, and enhances the identification of high-density monitoring points, leading to more accurate surface deformation assessments.

For high-resolution squinted airborne synthetic aperture radar (SAR) imaging, both linear range walk correction (LRWC) and motion error introduce significant azimuth spatial-variant (ASV) characteristics in the radar echo, rendering the classical assumption of "azimuth translational invariance" no longer valid. Existing sub-aperture methods attempt to overcome the ASV characteristics of the signal by performing segmentation processing in the data domain or the image domain. However, grating lobes or image stitching problems inevitably occur in the focused images. Existing full-aperture methods, on the other hand, utilize azimuth resampling or nonlinear chirp scaling (NCS) to address the ASV problem. Nevertheless, the above-mentioned methods basically handle the ASV characteristics introduced by LRWC and motion errors separately, without considering the coupling characteristics between the two. Therefore, this paper proposes a high phase-preservation squint airborne SAR autofocus imaging method by modifying the traditional azimuth resampling processing, so that only a single azimuth resampling factor is required to simultaneously solve the ASV problems brought about by LRWC and motion errors. The imaging processing results of airborne squint SAR real-data verify its good focusing effect. Meanwhile, the interferometric processing results of multi-pass cross-track SAR real-data also indicate that the proposed algorithm exhibits a high phase-preservation capacity. The images processed by the proposed algorithm and the comparison algorithms, as well as the multi-pass cross-track SAR complex images after registration, can be downloaded from https://pan.baidu.com/s/1okgAkp18ynK7qzKXe2lceQ?pwd=nquf.

Multichannel interferometry synthetic aperture radar (InSAR) systems enable the reconstruction of terrain height profiles by integrating multiple interferograms obtained from multifrequency or multibaseline configurations. In this paper, we present a robust redundant remainder number system (RRNS) specifically designed for the high-precision determination of terrain height profiles. The proposed method consists of two main steps: First, erroneous remainders are clustered, and the common remainder is estimated optimally. Next, the integral portion is determined using the RRNS. Furthermore, we derive a robust estimation condition that generalizes existing results. To apply the proposed method to real data, we have extended the robust RRNS technique to accommodate practical data conditions. The main improvements are as follows: First, the phase unwrapping model for real numbers is adapted to the integral case by selecting suitable prime numbers. Second, the process of selecting the optimal reconstruction result is enhanced by incorporating redundancy congruence, which involves using two equations for each case. Simulation results demonstrate that the extended method outperforms both the least squares method and the minimum cost flow method.

In recent years, the ground Cartesian back-projection (GCBP) algorithm has demonstrated significant advantages for bistatic forward-looking synthetic aperture radar (BFSAR) imaging with arbitrary geometries and complex configurations, primarily due to its interpolation-free operation. However, airborne BFSAR systems must additionally address motion error compensation challenges. Implementing effective motion compensation (MoCo) within the GCBP framework for BFSAR presents two key challenges: 1) The forward-looking configuration induces severe image spectrum tilt and nonsystematic range cell migration (NsRCM), significantly degrading phase error estimation accuracy; and 2) Spectrum resampling during BP processing obstructs direct time domain phase error (TDPE) estimation from the image. To address these challenges, this paper proposes a phase error reverse recovery method based on ground combined beam coordinate (GCBC) for BFSAR. The proposed MoCo method establishes the GCBC system aligned with the echo signal’s azimuth Doppler variation, which eliminates image spectrum tilt and reduces NsRCM caused by the bistatic configuration. Within this system, we introduce the spectrum center correction and spectrum tilt correction, which effectively remove image spectrum aliasing and enable accurate image domain phase error (IDPE) estimation. Furthermore, an analytical reverse recovery relationship between IDPE and TDPE is derived. These stages significantly enhance the accuracy and robustness of BFSAR motion error estimation. Simulation and real data results demonstrate the proposed method’s superior performance.

Forest height is a critical component of ecological and environmental assessments, playing a vital role in modern forest management, biomass estimation, and climate modeling. This manuscript presents a novel single polarization forest height inversion (SPFI) method that uses only single polarization interferometric synthetic aperture radar (InSAR) data without the assistance of auxiliary information. In the SPFI method, the probability density functions (pdfs) of forest height and terrain phases are constructed, followed by the estimation of the differences between adjacent forest heights using the phase gradient, and then the absolute forest heights are obtained by the integration of the relative forest heights. The effectiveness of the SPFI method is validated through experiments conducted at three distinct test sites, using airborne P-band InSAR data and spaceborne L-band InSAR data.

Existing deep learning-based methods for synthetic aperture radar (SAR) target recognition typically rely solely on the amplitude images without considering the complex characteristic of SAR images, making it difficult to recognize SAR targets with high visual similarity. To solve this issue, a novel dual-stream manifold multiscale network fused with electromagnetic features, i.e., EFMM-Net is proposed for target recognition in complex-valued SAR images. In EFMM-Net, the attributed scattering center (ASC) model is first utilized to reconstruct the complex-valued SAR image, thereby highlighting the electromagnetic scattering features of the target. Subsequently, the reconstructed complex-valued SAR image is combined with the original one to construct the dual-stream input. Second, a scattering-guided manifold multiscale (SGMM) backbone is proposed for parallel extraction of data features and electromagnetic scattering features of the target from the dual-stream input. During feature extraction, the SGMM backbone can effectively leverage the phase information of complex-valued SAR images and inject target scattering information into data features through scattering-guided channel-wise feature alignment, thus enhancing the awareness of data features to critical scattering characteristics. Finally, to effective fuse the data features and electromagnetic scattering features, a location awareness feature fusion (LAFF) recognition module is proposed. By exploiting coordinate attention, LAFF utilizes the target location information captured from electromagnetic scattering features to direct the feature fusion process, thereby increasing the focus of fusion features on the target region. The extensive recognition results of three-class and six-class ship targets in the OpenSARShip 2.0 dataset demonstrate the effectiveness and superiority of the proposed method.

In recent years, deep learning (DL) has achieved remarkable success in classifying hyperspectral images (HSIs), relying heavily on the quantity and quality of labeled samples. However, obtaining sufficient labels for HSIs poses a challenge. HSIs obtained by the same sensor often exhibit similar spectral information due to their shared physical, chemical properties, or reflective attributes. Joint analysis of several HSIs enables the integration of limited labeled samples and extraction of more robust and discriminative features from different HSIs. Therefore, a multitask collaborative network (MTCN) for the joint classification of multiple HSIs acquired by the same sensor in different areas is proposed. In the MTCN, each HSI has its own feature extraction channel, which facilitates the learning of image-specific representations. In addition, a feature sharing channel (FSC) is created to extract and transfer multihierarchical image-shared representations between multiple HSIs, thereby forming a common knowledge pool to facilitate feature sharing. Furthermore, a cross-channel mutual attention module (CMAM) is designed to collaboratively utilize features from image-specific and image-shared channels, enhancing the efficiency of information communication in HSIs. The experimental results on six HSIs demonstrate that the proposed MTCN can jointly classify multiple HSIs by the same sensor in different areas and achieve good classification performance.

High-resolution radar imaging with compressive sensing (CS) is significantly important and meaningful in practical applications, such as data collection burden reduction and resource allocation scheduling in a multifunctional radar. The class of matrix completion (MC) methods is a powerful tool to directly reconstruct the missing data to be applied in sparse radar imaging, which can overcome the discrete error drawback of traditional dictionary-based CS methods. In this article, we extend the MC method to tensor completion (TC) with multidimensional data representation, and a novel manifold low-rank and sparse TC (MLRSTC) radar imaging algorithm is proposed for enhanced sparse imaging performance. In the scheme, an attractive tensor radar data model is proposed, and the low-rank tensor property is discovered by capturing the latent and intrinsic data structure in high dimensions. In particular, the low-rankness superiority of the tensor model is confirmed by both the theoretical derivation and experimental analysis. Then, the Kronecker-basis-representation (KBR)-based tensor sparsity model is applied to format the proposed MLRSTC algorithm of sparse radar imaging, which can effectively promote the reconstruction of tensor data with enhanced low-rank property. Meaningfully, the proposed MLRSTC algorithm can work well under the condition of different sparse data sampling patterns. Next, the proposed MLRSTC algorithm is efficiently solved in an iterative manner under the framework of alternating direction method of multipliers (ADMMs) by updating the involved parameters in a closed-form solution. Finally, the experiments using both electromagnetic simulation and measured data are performed to confirm the effectiveness and superiority of the proposed MLRSTC algorithm beyond state-of-the-art (SOTA).

The differential interferometric synthetic aperture radar (DInSAR) technique can estimate the Earth’s surface displacement theoretically at centimeter- or millimeter-level accuracy, where the 2-D phase unwrapping (PU) is ineluctable, so that improper PU algorithm would deteriorate the accuracy. Conventional single-baseline (SB) PU-based DInSAR cannot accurately monitor high-gradient deformation due to the limitation of the phase continuity assumption. The conventional multibaseline (MB) PU-based DInSAR, including multifrequency-based two-pass DInSAR and two-stage programming approach (TSPA)-based three-pass DInSAR, is capable of delineating high-gradient deformation but imposes stringent requirements on InSAR data. Under this condition, we present a multitemporal baseline PU approach (MTBA) for two-pass DInSAR from single radar system such that even high-gradient deformation can be delineated at centimeter- or millimeter-level accuracy. The MTBA demonstrates to be valid through a simulation experiment and three strike-slip earthquake events. Furthermore, the MTBA expands the perpendicular baseline-based MB PU for topography mapping into the temporal baseline-based MB PU domain for deformation monitoring, potentially enriching the MB PU theory and extending the application of DInSAR technique.

The hybrid along-track (AT)/cross-track (XT) synthetic aperture radar interferometry (InSAR) system enables the measurement of radial sea surface velocity, where solving it through phase unwrapping (PU) is intrinsically ill-posed due to the coupling of velocity-induced and height-induced phase components. Conventional hardware-based methods impose stringent and costly system requirements, while auxiliary-data-dependent approaches are error susceptible. Under this condition, we innovatively propose an along-track two-stage programming approach (AT-TSPA) multibaseline (MB) PU method within the three-pass differential InSAR (DInSAR) framework. AT-TSPA addresses the ill-posedness by making use of the normal baseline diversity, thus enabling accurate and robust retrieval of sea surface velocity without relying on hardware upgrades or external auxiliary data. Both theoretical analysis and experimental results demonstrate that AT-TSPA is effective and practical for accurately measuring sea surface velocity under complex oceanic conditions. AT-TSPA is also applicable to other fields involving coupled velocity and height phase components, such as sea ice velocity estimation. Furthermore, AT-TSPA extends the theory of TSPA-based MB InSAR from terrestrial to oceanic domains, thereby advancing the applicability and practicability of well-posed InSAR techniques.

Airborne synthetic aperture radar (SAR) imagery is susceptible to non-systematic motion errors, which will definitely defocus the target image and degrade the recognition accordingly. Representations learned from conventional convolutional neural networks (CNNs) do not emphasize much about the intrinsic features of the data distribution, which collapses the purposefulness of feature extraction. To this end, a deep Merged Auto-Focusing Network (MAFNet) is proposed for adaptively removing the defocusing effect from the input SAR data used for target recognition. Specifically, we propose an end-to-end architecture consisting of one focusing module and one recognition module. The focusing module contains a U-shaped sub-network based on the cross convolution to ensure the phase history coherence of the extracted features, and a deep unfolding method is devised to improve the mathematical generalization of focusing and sparse features so as to enhance the purposefulness of feature extraction. In particular, a compact surrogate function is designed for the non-convex feature quantization problem in the focusing module, which leads to closed-form solutions. The recognition module simply consists of a classifier. By building a multivariate loss function consisting of a cross-entropy loss function and a novel focusing loss function, MAFNet achieves accurate target recognition even when the input data is contaminated by non-systematic phase errors and additive noises. MSTAR data set is utilized to validate the effectiveness of MAFNet, and comparisons with conventional algorithms are performed to demonstrate the superiority of the proposed network.

Accuracy assessment of interferometric synthetic aperture radar (InSAR) products without external reference data (ERD) has been a long-standing challenge because traditional phase unwrapping (PU) is an ill-posed problem. The limitations in accuracy assessment make it impossible to verify the precision of the PU results under actual observation conditions, so that the reliability of InSAR products in practical applications is unknowable. However, multibaseline (MB) PU is well-posed, so its accuracy can be evaluated in a statistical sense without using ERD, i.e., even if there are no in situ data, the accuracy of the products generated by MB InSAR can still be assessed theoretically. In this article, by obtaining the closed form optimality condition of the Chinese remainder theorem (CRT) optimization model, the new independent quantitative index for MB PU accuracy evaluation was mathematically established. Interestingly, we found that: 1) the optimality condition is a sufficient and necessary condition for the accuracy assessment of the MB PU and 2) it is affected by the normal baseline lengths of the MB InSAR system and the interferogram noise intensity. To practically apply this mathematical condition, a deep convolutional neural network (DCNN) was developed to refine MB InSAR product accuracy. The validity and effectiveness of the proposed approach have been systematically verified using simulated and acquired interferometric datasets.

Phase unwrapping (PU) is a critical step in interferometric synthetic aperture radar (InSAR) data processing. Among all PU methods, multibaseline PU (MBPU) methods is a state-of-the-art method, which can overcome the limitations of the phase continuity assumption in the traditional single-baseline PU methods. However, the MBPU methods still cannot effectively balance PU accuracy and efficiency when processing large-size interferograms. In particular, the current best MBPU methods, two-stage programming approach (TSPA), cannot work well when the baseline ratio is less than 2, limiting its application. To solve this problem, a WaveCluster-based robust and fast MBPU algorithm (WCRFPU) is proposed in this paper. First, appropriate initial grid and neighborhood parameters are selected according to the exclusive information of the InSAR data set to reduce the number of wrong clusters caused by dimension mismatch. Then the WaveCluster algorithm is used to cluster the intercept map with 3D clustering features, which can obtain more accurate clustering results and efficiently handle large-size interferograms. Subsequently, a cluster correction step is added to improve the PU accuracy further. Theoretical analysis and experimental results show that this method has more advantages than the existing MBPU methods in efficiency, accuracy, and adaptability to baseline ratios when processing large-size interferograms.

Pixel similarity measurement is a critical step in distributed scatterer (DS) interferometry, directly affecting DS phase estimation. Despite considerable efforts to improve its accuracy, existing methods still suffer from unsatisfactory performance, especially with small stack sizes. In recent years, deep neural networks have achieved remarkable breakthroughs in interferometric synthetic aperture radar (InSAR) processing. However, their potential for measuring pixel similarity in multitemporal InSAR remains unexplored. This article proposes a neural network-driven pixel similarity measurement approach, termed PSMNet. To address the challenge of accurately defining true data, a supervised learning strategy is designed. The proposed network consists of two main modules: 1) a feature extraction module that generates high-level feature images with enhanced representation and reduced noise and 2) a similarity measurement module that evaluates pixel similarity without relying on assumptions about data distribution. The network is trained on synthetic data, enabling it to generalize for different stack sizes and target characteristics. Extensive experiments on simulated and real TanDEM-X images demonstrate a significant accuracy improvement of the proposed approach, highlighting its robust performance for varying stack sizes and computational efficiency advantage compared to traditional methods. The proposed approach further enhances DS phase estimation and increases the number of measurement points, showing great promise for ground surface deformation monitoring.

Phase unwrapping (PU) is a critical process for numerous synthetic aperture radar interferometry (InSAR) applications. The advent of deep learning (DL) has revolutionized PU, with various DL-based methods emerging over the past four years that consistently achieve state-of-the-art results. However, the generalization capability of these methods is impeded by the lack of a large-volume training dataset for InSAR PU. In contrast, model-based PU methods, both single-baseline (SB) and multibaseline (MB), utilize mathematical formulations that represent the PU knowledge, often resulting in robust generalizability in their respective domains. This article introduces MoDL-PU, a hybrid model-based/DL-based PU method. MoDL-PU, leveraging the Res-UNet-Inception architecture, employs a two-stage training approach: initial dataset-based training to extract low-frequency unwrapped phase information, followed by retraining with three specialized PU knowledge to enhance high-frequency details for targeted PU tasks: SB PU (MoDL-SBPU), MB PU for Digital Elevation Model (DEM) reconstruction (MoDL-MBPUT), and MB PU for deformation monitoring (MoDL-MBPUD). The proposed method exhibits robust generalizability, interpretability, and noise resilience, effectively combining the advantages of model-based and DL-based PU methodologies. The experimental outcomes demonstrate that MoDL-PU not only exceeds the performance of conventional model-based PU methods but also competes favorably with state-of-the-art supervised and self-supervised DL-based approaches.

The elevation data obtained from radar altimetry can assist interferometric synthetic aperture radar (InSAR) technology in achieving more accurate absolute height calibration in generating digital elevation model (DEM). The traditional height calibration method determines the calibration constant by comparing the InSAR DEM with the reference DEM after InSAR generates the DEM. This paper proposes a calibration method during the phase signal processing that not only accomplishes height calibration but also helps InSAR break the phase continuity assumption using radar altimetry to obtain accurate absolute phase, thereby improving DEM product quality. Experiments conducted in the southern region of Greenland demonstrate that the integration of radar altimetry data facilitates the seamless combination of InSAR phase unwrapping and height calibration.

Polarimetric Interferometric Synthetic Aperture Radar (PolInSAR) possesses unique advantages in forest parameter retrieval due to its all-weather, all-day observation capability and effective acquisition of vertical structure information of ground targets. Based on the Random Volume over Ground (RVoG) model, the existing three-stage method fits the coherent line to estimate the ground phase. However, the accuracy of tree height inversion is restricted by noise during the estimation process. A new ground phase estimation method was proposed by fitting coherent lines using multiple pixels, improving the SNR. Results demonstrate that, compared to the existing three-stage algorithm, our method performs better in the tree height inversion of managed and natural forests.

Polarimetric Interferometric Synthetic Aperture Radar (PolInSAR) is a combination of polarimetric SAR and interferometric SAR, possessing both the sensitivity of interferometric SAR to the vertical information of objects on the ground and the sensitivity of polarimetric SAR to the geometric morphology and dielectric constant of objects. Therefore, it is a crucial technology for inverting forest structural information.Currently, the mainstream approach for forest tree height inversion continues to explore the role of polarimetric information in the inversion process. However, the important role of interferometric SAR in this process is often overlooked. This paper innovatively proposes the estimation of the tree height gradient maximum likelihood function. It introduces a Maximum Likelihood approach for Tree-height Estimation (ML-TE) that directly extracts tree height information from interferograms. Experimental results demonstrate the effectiveness of this method in tree height inversion.

Synthetic Aperture Radar (SAR) are fundamental tools for target classification and detection in the different applicative scenarios (military, agriculture, etc…). Extracting geometrical features of a target strongly help in its detection and classification. Indeed, the extraction of Attribute Scattering Center (ASC) characteristics is widely used from improving SAR target recognition. ASC extraction is a challenging task that requires the accurate estimation of tiny details (shape, orientation, etc…) from the SAR target backscattering. In this work, the aim is to exploit the potential of deep learning for ASC extraction. Considering a simulated environment, a deep-learning based classification solution is defined for extracting the target characteristics.We proposed a multi classification heads VGG solution, which can extract scattering parameters from complex images and also guarantee the estimation accuracy.

Deep learning has been widely applied to phase unwrapping in interferometric synthetic aperture radar (InSAR), particularly through one-step unwrapping using autoencoders in a regression approach to directly obtain the absolute phase from the wrapped phase, known for its robust performance. While most methods utilize l1or l2norms as loss functions, the Multi-Scale Structural Similarity (MS-SSIM) loss function has also demonstrated excellent performance. However, a critical issue that has been overlooked is that the absolute phase is a relative value, and its overall shift, which can be corrected by adding or subtracting a constant, does not impact the final outcome. Current loss functions, including the state-of-the-art MS-SSIM, heavily penalize this overall shift in the predicted result, which can be detrimental to the learning process in phase unwrapping tasks and may even misguide the optimization direction of neural networks. To address this concern, we have developed a novel loss function for phase unwrapping tasks, combining the contrast and structure scores from MS-SSIM with a newly designed relative difference loss. Experiments indicate that this loss function significantly outperforms the state-of-the-art MSSSIM loss function.

Polarimetric Synthetic Aperture Radar (PolSAR) data plays an important role in Earth observation. In this field, deep learning (DL) method can achieve high classification performance on PolSAR image dataset and, in particular, vision transformer(ViT) has achieved significant breakthroughs. Compared with convolutional layers, ViT is able to extract global feature and find the global relationship, which can help to improve the performance of classification. The aim of this work is to exploit the potential of ViT for PolSAR classification. In this case, we propose a simple classification method based on transformer, called Pol-Trans. The PolSAR data is pre-processed to get the coherency matrix. Then the image patch of the pixel to be classified is flattened as the tokens. Finally, with the class embedding, our transformer can output the classification result of the PolSAR data. Our experiments on the ALOS2 PolSAR dataset of San Francisco shows the effectiveness of our method.

Adaptive multilooking applied to multiple synthetic aperture radar (SAR) observations has been proven to be an effective process to improve the quality of multitemporal interferometric SAR (InSAR), in which the key task is to select the statistically homogeneous pixels (SHPs). The existing algorithms are mainly based on time-series information from the same position and perform unsatisfactorily when image number is small. In this study, we propose an adaptive multilooking approach based on the context covariance matrix for SHP selection, named CCM-SHPS. The core idea is to exploit spatially adjacent pixels to enhance the information volume. The context covariance matrix is constructed and the Wishart statistic test is employed to measure the similarity. The proposed CCM-SHPS is validated by a simulated stack on the filtered InSAR results, including the amplitude, interferometric phase, and coherence, demonstrating its advantage over five representative algorithms in speckle suppression and edge preservation.

Phase linking is a key step in distributed scatterer interferometry (DSI), which can significantly reduce decorrelation by retrieving a consistent phase series. The performance of phase linking can be severely degraded by the inaccurate coherence magnitude matrix. Recently, some studies proposed to mitigate the problem by employing the regularization methods, e.g., adding a quantity to the diagonal or shrinking to the identity matrix. However, the correction is insufficient due to the simple structure assumption. In this study, we propose a new phase linking approach based on a powerful regularization method. Specifically, it achieves the maximum likelihood estimation of the coherence matrix under the structural constraint of total positivity. A simulated stack is exploited to test the performance of the proposed approach. The qualitative and quantitative evaluations demonstrate its superiority over the existing regularization methods.

The microwave photonic synthetic aperture radar (SAR) is capable of realizing large scene remote sensing observation with centimeter or even millimeter resolution, which greatly enhances the ability to acquire target information. A key issue in airborne microwave photonic SAR imaging is how to accurately correct the two-dimensional (2-D) spatial variation characteristic of the motion error. The typical two-step motion compensation (MoCo) method cannot correct the azimuth spatial variant characteristic of motion error, and the traditional subaperture methods may introduce the problems of grating lobes and image stitching. In addition, the efficiency of existing parametric full-aperture autofocus methods is usually low. To solve the above problems, a nonparametric full-aperture autofocus method based on a two-stage processing framework is proposed in this article. The first stage is to introduce a nonparametric low-order nonlinear chirp scaling (NCS) or resampling (RS) model to compensate for the low-order spatial variant motion error that accounts for the dominant component before the range cell migration correction (RCMC), which ensures that there is no significant residual RCM after the RCMC. The second stage introduces a nonparametric high-order NCS/RS model after the RCMC to compensate for the remaining high-order azimuth spatial variant phase error to achieve accurate azimuth focusing. Based on the full-aperture processing strategy, the algorithm proposed in this article avoids the problems existing in the subaperture methods. In addition, the nonparametric modeling is used throughout the autofocus processing (e.g., motion error estimation and parameter reversion of NCS/RS model), which greatly improves the efficiency of autofocus processing. The results of processing simulated and measured data verify the effectiveness of the proposed algorithm.

Interferometric synthetic aperture radar (InSAR) images are severely corrupted by noise in both magnitude and phase. It is significantly essential to recover the true interferometric phase during InSAR signal processing. Usually, traditional phase denoising methods are to find homogeneous samples for filtering with the need to balance noise reduction and phase preservation, which may be a problem in dealing with topography scenes. In this article, a novel algorithm of robust nonlocal tensor decomposition (RNLTD) for InSAR phase denoising is proposed. In the scheme, a nonlocal tensor (NLT) model of the interferogram is constructed by selecting and stacking similar image patches in a nonlocal region. Benefiting from the simultaneous use of nonlocal and tensor tools, superior low-rank properties of this NLT can be acquired, which is also confirmed by numerical analysis. Then, a robust tensor decomposition algorithm is proposed to formulate the low-rank recovery of the interferogram and constrain the sparse outliers for noise reduction. Next, an alternating direction method of multipliers (ADMM) solution is applied to robustly and accurately restore the noise-reduced interferometric phase. As a result, the proposed RNLTD algorithm takes advantage of effectively capturing the phase structure in a high-dimension manner, which is helpful in phase preservation with the achievement of excellent noise reduction. Lastly, the experimental analysis using one set of simulated and two sets of measured InSAR data is performed to show the promising performance of the proposed algorithm.

With the launch of a number of multipolarimetric synthetic aperture radar (SAR) satellites, many multipolarimetric phase estimation algorithms have been introduced to reduce the decorrelation of distributed scatterers. They typically perform the traditional phase estimation on complex coherence matrix. Thus, the primary focus lies in accurately estimating the complex coherence matrix to achieve precise phase estimation. In this paper, we propose a multipolarimetric phase estimation approach with improved coherence matrix estimation, termed MPPE-CME. It includes two major steps. The first step is to select the polarimetric interferometric pairs using our proposed selection algorithm, which is adaptive and without setting any empirical parameters. In the second step, based on the selected polarimetric interferograms, we develop a dominant scattering mechanism (SM) extraction algorithm to estimate the complex coherence matrix with enhanced accuracy. The simulated experiment validates the effectiveness of the proposed polarimetric interferometric pair selection and dominant SM extraction algorithms. The real data experiment conducted at the Chengdu Tianfu International Airport demonstrates that MPPE-CME outperforms other multipolarimetric phase estimation algorithms with significantly reduced reconstructed phase noise, increased measurement point density, and improved deformation accuracy.

Distributed scatterer interferometry (DSI) is a well-known technique for ground surface deformation monitoring. Central to this process, phase estimation reconstructs a consistent phase series from all interferometric combinations. In theory, the maximum likelihood estimator (MLE) is the optimum approach for phase estimation. However, in practice, its performance is often compromised. Previous studies have demonstrated that the coherence magnitude bias is a source of error. However, other sources of error in the MLE processing remain unclear. This study systematically assesses the sources of error in phase estimation and develops a hybrid approach that corrects three identified sources of error: 1) To address the error from inhomogeneous pixels, an algorithm based on the covariance matrix preestimation and general likelihood ratio test (CMGLR) is developed to select more accurate homogeneous pixels; 2) to mitigate the bias from coherence magnitude matrix, we apply the oracle approximating shrinkage (OAS) algorithm to estimate the precision matrix with higher accuracy; and 3) to tackle the noise from interferometric phase matrix, the filtering principles are defined and the covariance matrix filtering (CMF) algorithm is designed to suppress the noise. A series of simulated experiments demonstrate the effectiveness of the proposed approach. Additionally, a real TanDEM-X experiment shows that the proposed approach can reconstruct the time series phase with reduced noise. Furthermore, the estimated deformation exhibits improvement with significantly increased measurement points MPs (>2.4 times) and higher accuracy compared to the traditional method based on the Kolmogorov–Smirnov (KS) test and sample covariance matrix (SCM). Particularly, it exhibits exceptional performance in monitoring fine structures, while the traditional method usually fails with very few MPs. These results underscore the significant potential of this approach in the realm of ground surface deformation monitoring.

Urban residents' daily lives and commerce depend on the reliable water and sewer pipeline network. Leaking the network is a nuisance, wasting precocious resources and money. Detecting and mitigating a leak in the network is essential for utility companies and the general public. As an ongoing study, we developed a U-net-based algorithm for leak detection and explored the possibility of understanding operations within the algorithm. As dimensionality reduction and feature extraction are the primary objectives of the convoluting and pooling processes in the algorithm, the processes can be carried out by principal components analysis (PCA). The algorithm then advances a leak/non-leak classification after extracting features. The support vector machine (SVM), one machine learning algorithm, can replace and perform the classification procedure. Thus, a (PCA+SVM) algorithm is developed, and more importantly, we interpret the studied U-net-based algorithm as a hybrid of the PCA and SVM. Finally, the (PCA+SVM) algorithm is evaluated in the leaking detection, and it satisfactorily detects a leak or non-leak location in urban areas of Tianjin, China.

Although the multi-baseline (MB) phase unwrapping (PU) approach does not rely on the phase continuity assumption embedded in the single-baseline (SB) PU approach, it is vulnerable to noise. The two-stage programming approach (TSPA) improves the noise robustness by using the gradient information of the interferogram. However, the TSPA is primarily designed for topography reconstruction. Then, we incorporate the temporal baseline into the TSPA to detect severe deformation, developing the time-series (TS) TSPA (TS-TSPA). The TS-TSPA estimates the absolute phase gradient by combing different temporal baseline lengths and then utilizes the L1-norm optimization model to obtain PU results. Two differential interferograms of 14 April 2021-20 May 2021 and 20 May 2021-1 June 2021 after the Maduo earthquake were showcased. The earthquake had a moment magnitude of Mw 7.4, occurring on 22 May 2021. The quake caused severe surface deformation, deviating or invalidating the phase continuity assumption. With successful PU results by the TS-TSPA, a fault line was identified, and estimated surface displacements ranged from −4.5 to 3.7 m along the line-of-sight (LOS) direction. The PU results of the SB PU method missed the fault line and only detected displacements between 0 and 1.3 m. Therefore, the TS-TSPA effectively detects significant surface deformation where the quake-induced damage could be devastating and outperforms the SB PU method to unwrap phases in damaged areas and fault line delineations.

A new method for monitoring the landslide percusor by soil moisture changes from closure phases is studied. The closure phases are created with an interferometric synthetic aperture radar (InSAR) dataset of triple pairs of interferometric phases. A closure phase of zero suggests no change, whereas a non-zero means change. Then, the decorrelation phases derived from the closure phases were separated by solving the linear programming (LP) convex problem. The decorrelation phase is linked to the soil moisture change. The method's effectiveness is demonstrated with the 2018 Baige landslide event and analysis of multi-temporal Advanced Land Observation Satellite-2 (ALOS-2) datasets. There was a drastic change in soil moisture before sliding. Thus, a new choice is provided for identifying potential landslide precursors by analyzing soil moisture changes.

Distributed scatterers (DSs) should be included in multitemporal interferometric synthetic aperture radar to improve the spatial density and quality of monitoring points. As a key step, phase estimation can significantly reduce the decorrelation of DSs by exploiting all available interferograms. The current phase estimation algorithms are known to be affected by the coherence bias. In this study, we propose an improved DS phase estimation approach, which uses a refined coherence bias correction algorithm. To demonstrate the effectiveness of the proposed approach, we apply it over 50 simulated synthetic aperture radar images. The coherence bias can be significantly reduced by the proposed approach, including an average coherence bias reduction of more than 35% over the existing bias correction algorithm. The reconstructed phase series obtained by the proposed approach have higher accuracy than the current methods.

Multibaseline (MB) interferometric synthetic aperture radar (InSAR) is an advanced variant of conventional InSAR that aims to enhance the accuracy and reliability of phase unwrapping (PU). Among the PU methods employed in MB-InSAR, the maximum likelihood (ML) method offers an optimal solution for phase estimation. However, its limited noise robustness has hindered its practical applicability. To address this limitation, we propose a novel approach, named InSAR phase probability density function (PDF)-to-height/deformation (PDF2HD), which leverages a newly introduced deep convolutional neural network (DCNN) with exceptional anti-noise capabilities. The PDF2HD method employs U-Net and residual network to estimate the InSAR PDF, enabling it to mitigate the influence of phase noise. We present experimental results using two simulated MB InSAR datasets to demonstrate the effectiveness of our proposed method for both digital elevation model (DEM) reconstruction and deformation monitoring.

The phase unwrapping (PU) for Permanent Scatterers (PS) is a key step to obtaining accurate urban mapping results (e.g., a height of a high-rise building) in the time-series InSAR workflow. The phase continuity assumption restricts the existing single-baseline (SB) PU algorithm, so it cannot obtain accurate results in an urban area with high-rise buildings. At the same time, the multi-baseline (MB) method has poor noise robustness for no use of global interferometric phase information. Here, an MB PU algorithm is proposed based on the two-stage programming approach (TSPA) and the general SB PU workflow for the sparse permanent scatterers. Then, we implemented the proposed method into the PSInSAR procedure and estimated building heights in urban areas of southern Chengdu, China. Satisfactory results were obtained for buildings with various heights as assessed by the Google Earth®image and in situ height measurements. Thus, the developed method is valid and effective in building height retrievals in urban areas.

Two-dimensional (2-D) phase unwrapping (PU) is an essential step in interferometric synthetic aperture radar (InSAR) analysis. Although theL0-norm PU method is desired, it is nondeterministic polynomial (NP)-hard. Thus, many PU methods have been proposed to find near-optimal solutions of theL0-norm. As PU is an ill-posed problem, it is difficult to choose the method with the most accurate solution unless reference data are available. In this letter, we prove that the NP-hardness of theL0-norm is weak, suggesting that the α-approximation algorithm of theL0-norm can be devised, i.e., the obtained near-optimal solutions can be within a factor of α of theL0-norm optimal value. The primary contribution of the proof is that the α value of each obtained PU solution can be considered as a new index to assess the PU performance without using reference data. The validity and effectiveness of the α-based index have been verified using simulated and acquired interferometric datasets and three PU methods.

At present, the resolution of the most advanced airborne microwave photonic synthetic aperture radar (SAR) can reach the order of centimeters or even millimeters, so the two-dimensional spatial variation and two-dimensional coupling characteristics of motion error will become more serious. In this paper, based on the advantages of nonlinear chirp scaling (NCS) and resampling (RS) processing, a microwave photonic SAR full-aperture autofocus algorithm based on a cascaded NCS-RS is proposed. Firstly, the proposed algorithm combines the typical two-step MoCo and chirp-Z transform (CZT) to correct the range spatial variant characteristics of motion error. Then, a cascaded NCS-RS processing is used to correct the azimuth spatial variant characteristics of motion error, in which NCS processing is introduced before range cell migration correction (RCMC) and RS processing is introduced after RCMC. Finally, the RS in cascaded NCS-RS processing is modified to change with range to correct the range-azimuth coupling characteristic of motion error. The three steps of the algorithm belong to the full-aperture processing, which avoids the problems of grating lobes and image stitching caused by the sub-aperture algorithm. The estimation of the parameters in NCS-RS processing is modeled as a high-dimensional optimization problem. Before solving this optimization problem, it is converted to multiple one-dimensional optimization problems. The results of processing simulated and measured data verify the effectiveness of the proposed algorithm.

Tomographic synthetic aperture radar (TomoSAR), which can provide three-dimensional (3-D) image of the observed scenes, has become an important technology for topographic mapping, forest parameter estimation, urban buildings modeling and etc. Recently, the developed compressed sensing (CS) and other similar methods have been widely applied for the achievement of super-resolution SAR tomography. However, there always exists inevitable model errors during the mining of scene information, such as discrete gridding on used dictionary and outliers among independent identically distribution (IID) samples, which tends to dramatically degrade the TomoSAR inversion. In this paper, a novel robust gridless CS (RGLCS) algorithm is proposed for high-resolution 3-D imaging of array TomoSAR. In the scheme, the atomic norm minimization (ANM) is used to model the joint-sparsity pattern on elevation distribution between adjacent pixels, which can be treated as gridless CS to avoid the discrete error of the dictionary. Meanwhile, the outliers and disturbances not satisfying the IID elevation distribution are modelled as sparsely distributed spike-noise in the image domain. The proposed RGLCS algorithm has the capability of perfectly separating the outliers and maintaining high-precision height resolution. For efficient solution, a fast alternative optimization is used to solve the objective function to effectively reduce the computational complexity. Next, the post-processing, including point cloud clustering and double-bounce scattering detection & eliminating, are studied to obtain high-resolution 3-D point cloud image. Finally, the experimental analysis using both simulated and measured data are performed to verify the effectiveness of the proposed algorithm. In particular, a practical demonstration using measured airborne array TomoSAR data is presented for urban mapping.

Multibaseline (MB) interferometric synthetic aperture radar (InSAR) is an extension of conventional InSAR and is used to improve phase unwrapping (PU) accuracy without obeying the Itoh condition. The Chinese remainder theorem (CRT) is the mathematical foundation of most MB PU algorithms for determining the connection between different MB interferograms. However, CRT only exploits the relationship between the interferometric phase and terrain height or surface deformation alone, i.e., the phases of topography and deformation are considered as the measurement biases for each other in the traditional processing chains. In other words, traditional MB InSAR cannot directly obtain InSAR products from interferograms that contain both the topography and deformation phases without external information or assumptions. To solve this issue, differing from CRT, this article presents a new mathematical framework for MB PU, which provides a likelihood function to jointly estimate the topography and deformation velocity gradient. Based on this framework, a novel MB PU method is proposed for simultaneously obtaining a digital elevation model (DEM) and deformation information from interferograms. The experimental results show that the proposed method is effective and efficient for DEM reconstruction and deformation monitoring.

In the small baseline subset (SBAS) algorithm, the zero-value closure phase assumption facilitates two-dimensional single-baseline phase unwrapping (PU) and then derives the surface deformation time series. The premise can fail when significant decorrelation occurs. Thus, we propose an optimization-based PU method by integrating the minimum-cost flow (MCF) model with the minimized closure phases. Three differential interferograms in 2017, i.e., 26 May-07 June, 07 June-19 June, and 19 June-26 May, Mao County of China, were unwrapped with the proposed method. The closure phases ranged from −6 to 7 rad, with an average of 0.01 and one standard deviation of 0.77 rad. Image cells having closure phases within ±1 rad are about 71%. Comparatively, closure phases of the MCF method were ±18 rad, with a mean of 0.55 and one standard deviation of 3.45 rad. Only ~30% of phase values were within ±1 rad. Hence, the studied PU method effectively minimizes the closure phases, thus potentially improving the deformation-related phase unwrapping used in the SBAS algorithm.

In a multi-temporal (MT) interferometric synthetic aperture radar (InSAR) algorithm, if the Itoh condition is not met, the closure phase of zero or near zero is no longer true. To resolve it, we apply a phase gradient network (PGNet) to assess a cell's phase gradient not subjected to the Itoh condition. The PGNet has been trained over rugged terrain in Mao County (32.06°N, 103.65°E), Sichuan Province, China. Then, the network was applied to predict phase gradients of three differential interferograms, i.e., 18 July-30 July, 30 July-11 August, and 11 August-18 July of 2017, Jiuzhaigou, Sichuan. A Ms (surface-wave magnitude) 7.0 earthquake (33.20° N, 103.82° E) occurred on 8 August 2017 in Jiuzhaigou. The PGNet has 1,175,000 cells with 0 for the horizontal closure phase gradient and 1,149,000 for the vertical closure phase gradient. (n = 1,413,120) For the Itoh condition-based method, the cell numbers are 984,800 horizontally and 1,094,000 vertically, less than those after the PGNet. Thus, the PGNet is more effective in minimizing the closure phase than the Itoh condition, improving an MT-InSAR algorithm's performance.

The Persistent Scatterer Interferometric Synthetic Aperture Radar (PS-InSAR) identifies persistent scatterers (PS) for surface deformation study. The selection of PS is important for obtaining reliable phase information. A novel deep convolutional neural network, namely PSNet, for identifying PS has been studied. The significant advantage of the PSNet lies in its deep architecture to learn characteristics of PS from enormous training images with different topography and landscapes. With the combined feature images composed of the average amplitude, amplitude dispersion, and coherence of interferograms as inputs, the PSNet was trained to classify the PS and non-PS. The results demonstrated that the PSNet delineated PS and non-PS pixels well. The number of PS obtained by the PSNet is more than doubled compared to the number of PS detected by the StaMPS algorithm.

Phase unwrapping is essential in interferometric synthetic aperture radar (InSAR) data processing. Currently, deep learning is widely used in the phase unwrapping process. For instance, the one-step phase unwrapping method is excellent because of its strong noise adaptability. The method treats the unwrapping process as a regression problem, which uses the l1 or l2 loss function to constrain the reconstructed phase to be close to the ground truth of the absolute phase. However, no matter whether the l1 or l2 loss function is used, the result may lack details in texture, and the details cannot be well preserved. This is because the l1 or l2 smoothens the output greatly, and the texture detail loss is not intentionally considered. Due to the noise of the wrapped phase, there is speckle noise in the valley part of the unwrapping result. To solve these problems, we study the generative adversarial network (GAN) with mixed loss functions. The texture details are preserved with the trained GAN, and the speckle noise in the valley is significantly reduced.

A deep convolutional neural network (DCNN) has been widely applied to the 2-D phase unwrapping (PU) in synthetic aperture radar interferometry (InSAR). Our previously-developed PGNet and BCNet outperform the model-based 2-D PU methods. However, the two networks can be further improved. As the PGNet is limited to estimating the phase gradients within ±2π, unwrapped phases can be incorrectly unwrapped sometimes. The BCNet is sensitive to the high-density distribution of the residues caused by a noisy interferogram, resulting in many isolated regions. To solve both issues, we bridge the PGNet and BCNet, studying a new DCNN-based 2-D PU framework (PG-BCNet). The results show that the PG-BCNet is more noise-robust than that of the BCNet and overcomes the limitation of the PGNet that cannot unwrap the phase gradients beyond ±2π.

Deep convolutional neural networks (DCNN)-based methods have been applied widely to ship detection in SAR images. However, most DCNN-based ship target detectors that focus on the detection performance ignore the computation complexity. We propose a lightweight anchor-free ship detection network (LASDNet) for SAR images to tackle this problem. First, a lightweight backbone utilizing a double fusion with squeeze-and-excitation-bottleneck block under the CSPNet design (CSP-DFSEB) and three pooling blocks (i.e., EVE, FCT, and ME blocks) are constructed, which achieves a balance between accuracy and efficiency. Second, a transformer-based aggregation layer conducts feature fusion. Finally, an improved one-stage anchor-free detector FCOS is presented. The analyses of the High-Resolution SAR Images Dataset for Ship Detection and Instance Segmentation (HRSID) dataset show that the proposed detector has the second least number of parameters (1.15 MB), the lowest computation complexity (1.01 GFLOPs), and the highest average precision (59.25) compared with other state-of-the-art methods.

The multi-baseline (MB) interferometric synthetic aperture radar (InSAR) technique is not subjected to the Itoh condition, i.e., phase continuity. The technique is particularly suitable to unwrap the wrapped interferometric phases and create a digital elevation model (DEM) in rugged terrain, where the permanent scatterers (PS) are usually scarce. This study shows that the technique satisfactorily unwrapped the wrapped phases with sparsely distributed PS and created a DEM for an area in Himalaya Mountain Range, China. In comparing three DEMs, two created by the single-baseline InSAR approach and one by the MB InSAR technique, the technique outputs the best DEM, as evaluated with a reference DEM.

Spaceborne synthetic aperture radar (SAR) real-time imaging is especially important for disaster emergencies and real-time monitoring applications with highly desired real-time requirements. Therefore, the continuous improvement of real-time imaging efficiency is an important development trend. At present, traditional real-time imaging algorithms based on constant pulse repetition frequency (PRF) have low accuracy when processing spaceborne SAR data with nonlinear trajectory. For this problem, the existing methods usually introduce some complex signal processing steps, such as scaling or interpolation processing, to improve the accuracy of the real-time imaging, but this will reduce its efficiency. Therefore, this article proposes a new real-time imaging algorithm based on variable PRF for nonlinear trajectory spaceborne SAR. By introducing the variable PRF, the proposed algorithm is equivalent to complete the complex signal processing steps in the radar signal transmission stage, which can greatly improve the efficiency of real-time imaging. Simulation experiments verify the effectiveness of the algorithm.

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

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$L^{p}$-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.

Considering that synthetic aperture radar (SAR) images obtained directly after signal processing are in the form of complex matrices, we propose a complex convolutional network for SAR target recognition. In this article, we give a brief introduction to complex convolutional networks and compare them with the real counterpart. A complex activation function is applied to analyze the influence of phase information in complex neural networks. Inspired by the theory of network visualization, a special kind of transfer learning based on the electromagnetic property from the attributed scattering center model is applied in our networks to modulate the first convolutional layer. The experiment shows a better performance in terms of classification accuracy compared to random weight initialization.

2-D phase unwrapping (PU) is one of the biggest challenges in synthetic aperture radar (SAR) interferometry (InSAR) processing. As an ill-posed problem, the performance of the traditional algorithmic model-based 2-D PU algorithms is not guaranteed to be correct with rapid ground deformation or topographic changes. An increasing number of remote sensing observations collected by different sensors (e.g., LiDAR and GPS) provides new opportunities to assist the traditional 2-D InSAR PU by reducing the nondeterminacy. In this article, we propose a novel knowledge-aided PU (KAPU) approach. KAPU compiles different prior knowledge from different sources with InSAR observations simultaneously through an integer programming model. More importantly, the mathematical proof demonstrates that the constraint of the optimization model of KAPU is totally unimodular, so KAPU can be efficiently solved without having to have the constraint that the ambiguity number is an integer. Theoretical analysis and extensive experimental results illustrate that KAPU outperforms the existing model-based 2-D InSAR PU algorithms on digital elevation model (DEM) generation and surface deformation estimation.

Interferometric phase denoising is a vital procedure for interferometric synthetic aperture radar (InSAR)-based remote sensing techniques because it can improve the accuracy of the final InSAR product. Here, we propose a deep convolutional neural network (DCNN)-based InSAR phase denoising method, abbreviated PDNet. Given an ideal wrapped phase, φ, the PDNet learns the self-similarity function of φ from the input interferogram. After training, the PDNet obtains filtered wrapped phases using the maximum-likelihood approach by exhausting all φs from –π to π. Unlike a boxcar-based filtering method, the PDNet does not consist of an “averaging operation” on the spatial domain, and the resolution loss and interferometric fringe distortion will not directly affect the PDNet result. Thus, the PDNet can be considered a nonlocal phase denoising approach. Analyses and results show that the PDNet is an almost near-real-time denoising algorithm. Its denoising accuracy is higher than that of the available model- and learning-based InSAR phase denoising methods.

Division-of-focal-plane (DoFP) polarimeter provides a way for snapshot acquisition, making it available to simultaneously record polarization measurements at different orientations. This polarization imaging system has gained more attention in the last few years and is promising to be used in the fields of computer vision and remote sensing. However, this system suffers from the degradation of spatial resolution. To reconstruct polarization information at full resolution, polarization image demosaicking is indispensable. To address polarization image demosaicking issue while preserving the essential structure of polarization data, a sparse tensor factorization-based model is proposed. For a target cube, its similar cubes are first grouped together as a tensor. Then, its compact dictionary and sparse core tensor are learned by factorizing the tensor using sparse coding. Moreover, the correlation among different polarization orientations and the nonlocal self-similarity are adopted to boost the performance. Experimental results on synthetic and real-world data demonstrate that our proposed model outperforms several state-of-the-art methods in terms of both quantitative measurements and visual quality.

Multibaseline (MB) phase unwrapping (PU) is a vital processing procedure for MB synthetic aperture radar interferometry (InSAR) signal processing and can improve the traditional InSAR by changing the ill-posed problem to the well-posed problem. The existing research has shown that the MB PU problem can be successfully converted into an unsupervised cluster analysis problem. Using the high feature descriptiveness of the deep learning technique, an unsupervised deep convolutional neural network, referred to as CANet, is proposed to cluster all the pixels into different groups according to the input’s recognizable pattern of the ambiguity number of the MB interferometric phase. Subsequently, we extend our previous two-stage programming-based MB processing approach (TSPA) to processing MB PU on a sparse irregular network, which is established from the clustering result of CANet. Both theoretical analysis and experimental results show that the proposed method is an effective MB PU method, and its execution time is drastically lower than those of many classical MB PU methods.

Two-dimensional (2-D) phase unwrapping (PU) is a critical processing step for many synthetic aperture radar (SAR) interferometry (InSAR) applications. As is well known, the traditional 2-D PU is an ill-posed inverse problem, which means that regardless of how skillful the PU algorithm designer is, it is impossible to design an algorithm that can correctly process all the 2-D PU situations, i.e., we can only design the best PU algorithm in the statistical sense. Therefore, accumulating PU processing experience from different study cases is important for PU algorithm design. Currently, the deep learning (DL) technique provides a potential framework to accumulate processing experience, and a flood of valuable data coming from different InSAR sensors provides the ability to enable the learning-based PU technique outside the traditional model-based technique. In this article, we transform the 2-D PU problem into a learnable image semantic segmentation problem and propose a DL-based branch-cut deployment method (abbreviated as BCNet). To start, we propose the optimal branch-cut connection criterion (referred to as OPT-BC) with the reference unwrapped phase given. Next, using the relationship between the residue and branch-cut as the learning objective, BCNet is trained using the samples provided by OPT-BC to produce the branch-cut result. Finally, the traditional branch-cut method is utilized to perform the postprocessing procedure to obtain the final PU result. The experimental results demonstrate that the proposed BCNet-based PU method is a near-real-time 2-D PU algorithm, and its accuracy outperforms the traditional model- and learning-based 2-D PU methods.

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.

In this paper the effectiveness of a CNN based interferometric phase unwrapping algorithm combined with phase noise filtering is analysed. In particular, the considered processing chain relies on a pre-processing step with the nonlocal filter InSAR-BM3D followed by a deep CNN solution for restoring the absolute phase. The analyses is conducted on simulated data with different coherence values and aims at comparing the performance of the unwrapping with and without the pre-processing step. This paper is the first step towards a unique deep learning solution for jointly unwrapping and restoring the absolute phase.

The recent, sharp increase in the availability of interferometric data captured by different synthetic aperture radar (SAR) interferometry (InSAR) sensors poses a new scientific question that whether there is a processing framework that can combine these observations to obtain a more credible InSAR product (i.e., digital elevation model (DEM) and surface deformation estimation). In this article, we extend our previous two-stage programming-based multibaseline processing framework for combining the interferograms generated from disparate InSAR systems with different system parameters to enhance the InSAR performance at the signal processing stage. The proposed multisystem interferometric data fusion framework, abbreviated as TSDFF, includes three processing steps: multisystem interferogram registration, multisystem phase unwrapping, and absolute phase fusing. The advantage of TSDFF is that it can allow the data sets from different InSAR sensors to help each other to get rid of the limitation of the Itoh condition so that the application scope of each InSAR sensor will be effectively enlarged (e.g., measuring violent surface change or mountainous DEM). In addition, to quantitatively analyze the measurement bias robustness bound of TSDFF, the TSDFF-Fusion theorem is proposed, which offers significant application guidance for TSDFF at different noise levels. The real and simulated experimental results reveal the effectiveness of TSDFF for fusing the data sets from disparate InSAR systems.

Phase unwrapping (PU) is a key step for the synthetic aperture radar (SAR) interferometry (InSAR). Single-baseline (SB) PU and multi-baseline (MB) PU are two independently developed technologies, each of which has its own advantages and disadvantages. A two-stage programming-based MB PU method (TSPA) proposed by Yu [1] establishes a connection between the MB and SB PU methods. TSPA breaks the limitation of the phase continuity assumption by using the Chinese remainder theorem (CRT), and uses the minimum-cost flow (MCF) optimization model to obtain the PU result. TSPA can be regarded as a framework for solving MB PU problems. In this paper, we studied how to transplant the infinity-norm ( L∞-norm) optimization model into TSPA framework. Under the TSPA MB PU framework, a L∞-norm based MB PU method (referred to as Inf-TSPA) is proposed to solve the problem of low PU accuracy of the L∞-norm SB PU method. The experimental results on the simulated and the realistic MB InSAR data sets verify that the performance of Inf-TSPA is significantly improved compared to the L∞-norm SB PU method.

Multi-baseline (MB) phase unwrapping (PU) is an exciting and growing technique in synthetic aperture radar interferometry (InSAR). It can overcome the limitation of the phase continuity assumption in the single-baseline (SB) PU. However, the performance of the MB PU is very sensitive to measurement bias. To overcome the shortness, a three-stage framework (TSF) is proposed, which combines the SB PU technique. In TSF, the interferograms are unwrapped firstly by a SB PU algorithm. Then, we utilize a machine learning algorithm to segment the blocky areas that have the same ambiguity number errors caused by the SB PU errors, and correct the SB PU errors by implementing an edge gradient MB PU technique. In the third stage, a traditional MB PU method is used to estimate the residual global ambiguity number. TSF fuses the SB and MB PU techniques effectively, and the theoretical analysis and experiments indicate that the proposed method can solve the MB PU problem with strong robustness and high computational efficiency.

Multi-baseline (MB) phase unwrapping (PU) is an important processing stage of MB synthetic aperture radar (SAR) interferometry (InSAR). Compared with the traditional single-baseline (SB) PU, MB PU is more applicable to the mountainous area, which does not follow the Itoh condition. A two-stage programming MB PU approach (TSPA) proposed by H. Yu, which builds the link between SB and MB PUs, so many existing classical SB PU methods can be transplanted into MB domain. In this paper, an extended Goldstein's Branch-cut algorithm for MB InSAR using the TSPA, abbreviated as TSPA-BC, is proposed, consisting of three steps. In step 1, the MB residues are identified according to the phase gradients estimated by TSPA based on CRT. In step 2, the MB branch cuts with global minimal length are generated, which is equal to the MB L° -norm branch-cut length. In step 3, the final PU result are obtained by a flood-fill integration process using the phase gradients obtained by stage 1 in which the integration path does not pass through any MB branch cut. The experimental results of TanDEM-X MB dataset illustrate that the effectiveness of the TSPA-BC method in the rugged area.

Two-dimensional phase unwrapping (2-D PU) is one of the key processes in reconstructing the topography or displacement of the Earth surface from its interferometric synthetic aperture radar (InSAR) data. Estimating the absolute phase gradient information is an unavoidable step utilized by almost all the 2-D PU methods. Traditionally, the gradient estimation step relies on the phase continuity assumption, which requests that the observed area has spatial continuity. However, the abrupt topographic changes and system noise usually results in the failure of the phase continuity assumption in reality. Under this condition, it is difficult for the traditional 2-D PU to provide the correct absolute phase over the area with abrupt interferometric fringe change or with strong system noise. To solve the issue, we propose a novel deep convolutional neural network (DCNN), abbreviated as PGNet, to estimate the phase gradient information instead of the phase continuity assumption in this article. The major advantage of PGNet lies in its deep architecture to learn the characteristics of phase gradients from enormous training images with different noise levels and topographic features. Subsequently, the L1-norm objective function is used to minimize the difference between unwrapped phase gradients and the gradients estimated by PGNet for obtaining the final PU result. Taking the phase gradient pattern of the TerraSAR-X-TanDEM-X interferogram as the learning object, experimental results demonstrate the absolute phase gradient estimated by PGNet is more credible than that from the phase continuity assumption such that the corresponding PU result outperforms those obtained by the traditional 2-D PU methods.

For the multibaseline (MB) synthetic aperture radar (SAR) interferometry (InSAR), MB phase unwrapping (PU) is an important step. With the rapid development of MB InSAR, the size of the datasets from the MB InSAR system is becoming increasingly larger. Under the situation of "bigdata", MB PU may face new problems with insufficient computing resources, or take too much running time to get the PU result. In order to deal with such case, we propose a convex hull and cluster-analysis based fast large-scale MB PU method (CCFLS) with enlightened by the single baseline (SB) PU method (CHFLS) from H. Yu [1]. CCFLS uses the clustering phenomenon of the MB residues to generate the convex hull of residues set with balance polarity, and avoids spending the computation resources on the area within the convex hull, so that the high-precision PU solution can be quickly obtained. The theoretical analysis and experiment results indicate that CCFLS can effectively reduce memory consumption and calculation time.

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.

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 Vu and Lan to the LS MB InSAR data set in this paper. To be specific, the MB Lκ-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 Lκ-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.

Multibaseline (MB) interferometric synthetic aperture radar phase unwrapping (PU) has the advantage of using the baseline diversity to increase the ambiguity intervals of the interferometric phases and overcome the limitation of the phase continuity assumption. One major challenge of the MB PU is that the performance of PU greatly depends on the baseline configuration. In this letter, the motion compensation algorithm is used to modify the baselines of the interferograms. Therefore, optimal baseline configuration can be used in the MB PU to improve the PU performance. Real ALOS/PALSAR data over Himalayan mountain area have been used to verify the performance of the proposed method. The experimental results show that the MB PU with modified baselines becomes more reliable.

2-D phase unwrapping (PU) is a critical image processing step in many interferometric measurement technologies. To avoid the discontinuous phase gradient error spreading from the noisy region to the high-quality region of input interferogram, a skillful PU method should keep the congruency between input phase fringes and rewrapped phase fringes of the PU result as much as possible. However, traditional PU methods often fail in case input interferogram contains “bad” regions, in which the phase information should not be trusted. Under this condition, it is desired that the PU method instinctively keeps the fringe-congruency in the high-quality area and reasonably modifies the input phase fringes in the low quality area. In other words, the PU method with an extra adaptive filtering function would be preferred in practice. Based on this perspective, a novel minimum infinity-norm-based PU method, referred to MIN, is proposed in this letter. Both theoretical analysis and experiments demonstrate that the MIN method is an effective PU method.

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.

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.

Two-dimensional phase unwrapping (PU) is a critical processing procedure of synthetic aperture radar (SAR) interferometry (InSAR). With the rapid advance of InSAR, the scale of the interferogram is becoming larger and larger. Under the condition of “big-data” PU, there are two new hurdles encountered: i) the dilemma between execution speed and accuracy, ii) the limitation of computing memory. To effectively solve these two problems, a new fast large-scale PU methodology, which is based on the convex hull algorithm and residue clustering characteristics, is discussed in this paper. The theoretical analysis and experiments indicate that this proposed large-scale PU methodology has some desirable potentials for large-scale PU problem: 1) peak memory consumption is very low which can avoid tiling processing; 2) time complexity is approximatively linear; 3) PU solution is as precise as some representative high accuracy PU methods.

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 L1-norm envelope-sparsity theorem, which gives a sufficient condition to exactly guarantee the consistency between local and global L1-norm PU solutions, is put forward and proved. Furthermore, the L0-norm envelope-sparsity theorem, which gives a sufficient condition to exactly guarantee the consistency between local and global L0-norm PU solutions, is also proposed and proved. Afterward, based on these two theorems, two tiling strategies are put forward for the large-scale L0-norm and L1-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 largescale L0-norm and L1-norm PU problems.

Multibaseline 2-D phase unwrapping (PU) is a critical step for the multibaseline synthetic aperture radar interferometry. Compared with the single-baseline PU, the multibaseline PU does not need to obey the phase continuity assumption, i.e., it is applicable to the terrain with the violent change. However, the performance of the multibaseline PU is directly related to noise level. In order to improve the noise robustness of the multibaseline PU, in this paper, we transplant the framework of the single-baseline PU into the multibaseline PU and propose a two-stage programming approach, referred to as TSPA, which makes use of the gradient information of the interferogram similar to how the conventional single-baseline PU method does. Fortunately, although the proposed method belongs to the integer programming (usually, the integer programming is an NP-hard problem which is hard to solve), the constraint of the optimization model of the TSPA method is unimodular, so it can be efficiently solved. Furthermore, interestingly, some useful and important concepts of the single-baseline PU, for example, residue and branch cut, are also transplanted into the multibaseline PU in this paper, and we discuss the potential of extending most of the representative single-baseline PU methods into the multibaseline domain as well. Finally, the experiment results show the effectiveness and noise robustness of the TSPA multibaseline PU method.

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 theL1-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.

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.

2-D phase unwrapping is an important technique in many applications. However, with the growth of image scale, how to tile and splice the image effectively has become a new challenge. In this paper, the phase unwrapping problem is abstracted as solving a large-scale system of inconsistent linear equations. With the difficulties of large-scale phase unwrapping analyzed, L(0)-norm criterion is found to have potentials in efficient image tiling and splicing. Making use of the clustering characteristic of residue distribution, a tiling strategy is proposed for L(0)-norm criterion. Unfortunately, L(0)-norm is an NP-hard problem, which is very difficult to find an exact solution in a polynomial time. In order to effectively solve this problem, equations corresponding to branch cuts of L(0)-norm in the inconsistent equation system mentioned earlier are considered as outliers, and then an outlier-detection-based phase unwrapping method is proposed. Through this method, a highly accurate approximate solution to this NP-hard problem is achieved. A set of experimental results shows that the proposed approach can avoid the inconsistency between local and global phase unwrapping solutions caused by image tiling.