Phase unwrapping using discontinuity optimization

Two-dimensional phase unwrapping (2-D PU) is a crucial step in interferometric signal processing. The accuracy of phase unwrapping (PU) will significantly affect subsequent processing. Existing algorithms perform poorly in areas with rapid terrain changes or with low coherence. In order to solve the above problems, this letter proposes a method of using a neural network to predict residuals, followed by the minimum <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L^{1}$ </tex-math></inline-formula> -norm algorithm for phase reconstruction. The network for predicting residuals is called residual prediction network (RPNet). To construct more complex loss terms, the continuous relaxation strategy is applied to its training. The proposed method overcomes the effects of noise and terrain changes due to the accurate prediction of residuals. The compensated phase gradients enable the minimum <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L^{1}$ </tex-math></inline-formula> -norm algorithm to reconstruct phases more accurately. The experimental results performed on simulation and interferometric synthetic aperture radar (InSAR) data demonstrate the effectiveness of the proposed method.

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

Phase unwrapping (PU) is one of the key processing step in reconstructing the digital elevation model (DEM) of a scene from interferometric synthetic aperture radar (InSAR) data. The PU problem entails the estimation of an absolute phase from the observation of its noisy principal (wrapped) values. This paper presents a 2D InSAR phase unwrapping algorithm exploiting the capability of the Kalman algorithm to simultaneously perform noise filtering and phase unwrapping. The performance of the proposed algorithm is tested on simulated InSAR images of the Gaussian type proving the effectiveness of our method.

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

To realize phase wrapped in the Interferometric synthetic aperture radar(InSAR), a hybrid phase unwrapping algorithm that combines the robust of the quality-guided method and more computationally efficient of the surface-fitting method is proposed in this paper. The algorithm utilizes different methods at different quality regions to achieve the phase unwrapping. The method uses quality-guided method to unwrap the phase in high quality regions, and uses surface-fitting method to obtain the surface of the unwrapped phase in remain regions. Moreover, genetic algorithm also be used to optimize the gradient error function, which can be minimized by optimizing the polynomial coefficients of the phase surface. Both simulated and experimental results have shown that the new algorithm can avoid the "isolated island phenomenon" successfully, and it is also especially appealing due to its computational efficiency and robustness when compared to other traditional methods.

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

In a typical interferometric synthetic aperture radar (IFSAR) system employed for terrain elevation mapping, terrain height is estimated from phase difference data obtained from two phase centers separated spatially in the cross-track direction. In this paper we show how the judicious design of a three phase center IFSAR renders phase unwrapping, i.e., the process of estimating true continuous phases from principal values of phase, a much simpler process that inherent in traditional algorithms. With three phase centers, one IFSAR baseline fan be chosen to be relatively small so that all of the scene's terrain relief causes less than one cycle of phase difference. This allows computation of a coarse height map without use of any form of phase unwrapping. The cycle number ambiguities in the phase data derived from the other baseline, chosen to be relatively large, can then be resolved by reference to the heights computed from the small baseline data. This basic concept of combining phase data from one small and one large baseline to accomplish phase unwrapping has been previously employed in other interferometric problems. The new algorithm is shown to possess a certain form of immunity to corrupted interferometric phase data that is not inherent in traditional 2D path-following phase unwrappers. This is because path-following algorithms must estimate, either implicitly or explicitly, those portions of the IFSAR fringe data where discontinuities in phase occur. Such discontinuities typically arise form noisy phase measurements derived from low radar return areas of the SAR imagery. When wrong estimates are made as to where these phase discontinuities occur, errors in the unwrapped phase values can appear due to the resulting erroneous unwrapping paths. This implies that entire regions of the scene can be reconstructed with incorrect terrain heights. By contrast, since the new method estimates the continuous phase at each point in the image by a straightforward combination of only the measured phases from the small and large baseline, phase estimation errors are confined to that point. We derive quantitative expressions for the new algorithm that relate the probability of selecting the wrong phase cycle to parameters of the interferometer. We then demonstrate that use of median filtering can very effectively mitigate those cycle errors that do occur. By use of computer simulations, we show how the new algorithm is used to robustly construct terrain elevation maps.© (1996) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

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

Phase unwrapping is an essential process in synthetic aperture radar interferometry that restores phase signals constrained within the range of (-π, π) to their true phase values. Traditional algorithm-based methods can introduce significant errors due to rapid and steep phase gradient or noise, which negatively impact terrain elevation and surface displacement analyses. To overcome these limitations, deep learningbased phase unwrapping techniques have been proposed; however, there has been insufficient previous studies due to the lack of accurate training and test data. This paper aims to share the training data generated using the phase unwrapping simulation method with locally-different phase noise. The data were generated by the simulation of topographic phases and phase noise, atmospheric and orbital distortions. Additionally, data augmentation for phase variation and noise levels was applied to address data imbalance issues. The shared data consists of two types: one with a constant phase noise level for each patch, and another that simulates locally different phase noise based on augmented coherence data. This data is primarily effective for unwrapping topographic phase components and holds significance as the first phase unwrapping training data of synthetic aperture radar interferograms shared in Korea. We expect this resource to serve as foundational data for future phase unwrapping technology research, including applications for upcoming satellites like KOMPSAT-6 and water resource satellites.

Two-dimensional phase unwrapping is a key step in the phase extraction process, an image-processing stage that is common to many different systems. Many varied approaches have been proposed over the past several decades. However, with the growth of image scale, it poses new challenges in terms of computational and memory requirements to phase unwrapping that require a global approach to obtain good results. Owing to only a single process used in most previous algorithm implementations, it becomes more problematic to unwrapping when the required computing resources exceed the capability of one computer. Meanwhile, with the development and application of supercomputer techniques, high-performance computing is emerging as a promising platform for scientific applications. In this paper, a novel hybrid multiprocessing and multithreading algorithm is proposed in order to overcome the problem of unwrapping large data sets. In this algorithm, we improve on Goldstein's branch-cut algorithm using simulated annealing idea to further optimize the set of branch cuts in parallel. For large data sets, the tiling strategy based on the nature of parallel computing guarantees the globality of phase unwrapping and avoids large-scale errors introduced. Using real and simulated interferometric data, we demonstrate that our algorithms are highly competitive with other existing algorithms in speed and accuracy. We also demonstrate that the proposed algorithm can be efficiently parallelized and performed across nodes in a high-performance computing cluster.

Synthetic Aperture Radar Interferometry (InSAR) has grown significantly over the past few decades, which were mainly used in remote sensing applications. Most InSAR applications (e.g., terrain mapping and monitoring) utilized a key technique called phase unwrapping Phase unwrapping obtained the absolute phase from the wrapped phase for the subsequent application. However, the collected wrapped phase inevitably contains noise due to the influence of factors such as atmosphere and temperature in the InSAR acquisition stage. This noise made it challenging to obtain the absolute phase from the wrapped phase. This study proposed a deep learning framework (PUnet) for phase unwrapping form InSAR data. pUnet was a robust framework using U-net as the basic structure combined with an attention mechanism and positional encoding, facilitating accurate phase unwrapping from the wrapped phase. Through comparative experiments with typical phase unwrapping algorithms, we demonstrated that pUnet could obtain absolute phases with high accuracy and robustness than from the wrapped phase under various levels of noise.

SUMMARY Two-dimensional phase unwrapping (PU) process usually causes a noise-induced distortion in the geographical information of a wrapped phase image obtained by, for example, interferometric synthetic aperture radar (InSAR). This paper presents a novel method to reduce the phase-unwrapping distortion by being based on two-dimensional fractional Brownian motion (fBm) theory. The method incorporates fractal geometry estimation with conventional global-transform PU. For the spatialfrequency spectrum of an observed phase image, we estimate the fractal dimension by assuming an almost constant dimension over the image. Then, according to the estimation, we compensate the distorted spectrum of the tentatively computed global PU result. We obtain a better topographical map as the inverse Fourier transform of the compensated spectrum. It is demonstrated that the proposed method increases the signal-to-noise ratio of PU results for simulated data with various noise levels. Evaluations on an actual InSAR phase image also show that the method significantly improves the quality of the conventional global-transform PU result, in par

Interferometric Synthetic Aperture Radar (InSAR) applies the interferograms of two or more SAR images to generate maps of surface deformation or digital elevation models. InSAR operational processing chain for displacement map generation comprises of five major stages: co-registration and re-sampling, interferogram generation, flat-earth correction, topography correction and phase unwrapping. This paper discusses and evaluates the authors' proposed algorithms for SAR image matching and for topographic and reference-phase corrections, which improve conventional InSAR processing techniques in terms of increasing efficiency and reducing the time and computational effort. Our proposed algorithms are implemented in MATLAB and evaluated with respect to the conventional InSAR processing performed by DORIS software for a pair of Envisat ASAR data associated with the 2003 BAM earthquake.

Phase unwrapping is the most difficult and unavoidable problem in the interferometric synthetic aperture radar (InSAR) processing procedures. Intensive researches have been done and the methods proposed were summarized into two categories: path following and minimum norm. Unwrapping result by path following is congruent with wrapped phase and require less time and memory. While minimum norm method usually could not obtain congruent result directly and take more computing resource. Weighting could improve phase unwrapping result very much if the suspicious region could be correctively separated out by weighting function. However, common used weighting such as coherence or phase gradient could not serve this purpose very well. In this paper, we proposed a novel method to unwrap phase, which combined the advantages of both categories, and set weight based on phase unwrapping consistence. We demonstrated the method with real InSAR phase. The unwrapping result showed the novel method could recover the dynamic range of phase than least square method while keep correct trend.

Many imaging systems, e.g., interferometric synthetic aperture radar (InSAR), yield phase images. These systems retrieve the phase up to a modulo-2π rad ambiguity, i.e., the phase is wrapped into the principal interval [Ȣπ π). Phase unwrapping (PU) is, then, a crucial inverse problem to obtain absolute phase, which is what embodies physical information. If the phase difference between neighboring pixels is less than π rad, then, phase unwrapping can be obtained unambiguously. This, however, is not always the case. For example, in InSAR, where absolute phase is proportional to the terrain elevation, we often face neighbor phase differences much larger than π rad. The PU problem is even more challenging for noisy images. This paper proposes a diversity approach, which consists of using two (or more) images of the same scene acquired with different frequencies. Diversity grants an enlargement of the ambiguity interval [−π π), thus, allowing to unwrap images with high phase rates. Furthermore, this paper presents a multi-resolution technique to make denoising. We formulate both tasks as integer optimization problems, which we tackle by using graph cuts techniques. We illustrate the effectiveness of our methodology by showing experimental results, which are, to our knowledge, state-of-the art competitive.