A Refined Cluster-Analysis-Based Multibaseline Phase-Unwrapping Algorithm

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.

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

Interferometric Synthetic aperture radar (InSAR) aided inertial navigation system (INS) is developed to introduce terrain elevation into registration, which gives out accumulated error of INS. Unwrapped InSAR interferogram plays a key role in previous InSAR/INS frameworks, while airborne and side-looking assumptions are usually made. However, phase unwrapping is time-consuming and high squint geometry with nonlinear trajectory is common for applications with InSAR/INS. In this article, a novel wrapped InSAR interferogram based positioning method for high-speed maneuverable platform is proposed. A novel back-projection based InSAR (BP-InSAR) signal model for slightly curved diving trajectory with high squint angle is firstly presented. Then process which generates phase gradient template from given DEM is presented, considering both the estimated and measured trajectories. Error analysis is also made to discuss the performance of the proposed method in single dual-channel observation. Finally, a sequential maximum likelihood estimator based on error analysis is implemented to deal with the remained uncertainty in single observation. Numerical experiments verify the proposed method and fully demonstrate the performance of it with curved trajectory and random errors in both position and attitude.

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.

Multi-baseline phase unwrapping with robust branch and bound pure integer programming algorithm

One major challenge of QRS wave detection is the deleterious impact of inevitable noise in electrocardiogram (ECG) signals, which can deteriorate the detection performance of algorithms. Previous research has shown a nonlinear monostable potential‐based algorithm for enhancing the QRS complex in a noisy environment. Its main mechanism is the stochastic resonance effect, which transfers noise energy to information‐carrying ECG signals in the nonlinear potential. However, the QRS detection algorithm based on monostable stochastic resonance (MSR) exhibits a limited noise margin to maintain extremely good performance. To further improve noise robustness, we propose a multi‐parameter constrained bistable SR (MCBSR) module for the QRS detection algorithm without requiring a large amount of training data. The MCBSR module can maximize the ECG signal while suppressing noise when there is a QRS complex and minimizes the ECG signal otherwise. Using four publicly available databases for testing, the MCBSR‐based QRS detection algorithm has been proven to achieve superior performance among state‐of‐the‐art algorithms. Compared to the conventional nonlinear method, the MCBSR enables the QRS detection algorithm to have significantly stronger noise robustness under various noise types. Therefore, this study successfully provides a more excellent nonlinear potential and greatly enhances the noise robustness of the QRS detection algorithm in large noise environments. © 2025 The Author(s). IEEJ Transactions on Electrical and Electronic Engineering published by Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

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

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

Implicit Neural Representations (INRs) have revolutionized signal processing and computer vision by modeling signals as continuous, differentiable functions parameterized by neural networks. However, INRs are prone to the spectral bias problem, limiting their ability to retain high-frequency information, and often struggle with noise robustness. Motivated by recent trends in iterative refinement processes, we propose Iterative Implicit Neural Representations (I-INRs). This novel plug-and-play framework iteratively refines signal reconstructions to restore high-frequency details, improve noise robustness, and enhance generalization, ultimately delivering superior reconstruction quality. I-INRs integrate seamlessly into existing INR architectures with only a 0.5–2% increase in parameters. During reconstruction, the iterative refinement adds just 0.8–1.6% additional FLOPs over the baseline while delivering a substantial performance boost of up to +2.0 PSNR. Extensive experiments demonstrate that I-INRs consistently outperform WIRE, SIREN, and Gauss across various computer vision tasks, including image fitting, image denoising, and object occupancy prediction.

In the field of optical interferometry, phase retrieval is a critical step in acquiring the phase information of fringes. Various deep-learning-based methods have been proposed for phase retrieval from a single-frame interferogram. However, the existing methods still cannot obtain the unwrapped phase directly without the aid of extra steps. To truly fulfill end-to-end phase retrieval for various fringe patterns, we propose a novel method with carefully crafted network architecture and training methodology. Experimental results on simulated and actual interferograms show excellent accuracy, noise robustness, and demodulation efficiency without any further phase unwrapping or polynomial fitting required by the existing methods. Furthermore, the proposed method is compatible with non-Zernike-polynomial-phase interferograms containing phase discontinuities. These properties have qualified the proposed method for high-standard interferometric measurement for optical fabrication.

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.

Clustering analysis is an important approach of data mining. This paper presents an ANN-based clustering analysis algorithm with dynamic data window (DDW). Comparing with k-means algorithm merged in density-based and integrated clustering analysis algorithm, the new clustering analysis algorithm based on artificial neural networks and combining with DDW has more valuable in data mining. This algorithm can immensely avoid the effect on accumulation points from boundary points, and can automatically find representative accumulation points in all kings of shapes. Furthermore its applications in CIS will be discussed in the paper. Some analysis results show the significant improvement to ship-routing design with the clustering analysis algorithm based on ANN and DDW in database of CIS.

Similarity and cluster analysis are important aspects for analyzing microarray data. Based on our perspective of viewing microarrays as time series data, both similarity analysis and cluster analysis are carried out through indexing on time series data using R*-Trees. We have developed algorithms for similarity and cluster analysis on microarray data, and conducted experimental studies and comparative studies. First, our study shows that principle components analysis (PCA) has superiority over several other methods (such as DFT and PAA) as far as distance conservation is concerned. A similarity analysis tool based on PCA has been developed, which is able to explore less R*-Tree nodes before finding its similar counterparts and returns less false positives than other methods. In addition, we also extend R*-Tree's application to cluster analysis. With the aid of R*-Tree indexing, two clustering algorithms. KMeans-R and Hierarchy-R, are proposed as an improved version of K-Means and hierarchical clustering, respectively. Experiments for similarity search and cluster analysis based on proposed algorithms have been carried out and have shown favorable results. Experiments related to yeast cell cycle dataset are reported in this paper.

The NORMIX data analysis program, which incorporates cluster analysis and multivariate statistical analysis routines, was modified and revised for use In a UNI VAC 1110 computer. The revised program was tested on three sample data sets and produced results in agreement with those from the original program. The NORMIX program was then used to evaluate and analyze eight sets of aerometric data from various sources. Comparison of the performance of NORMIX with two other cluster analysis algorithms, MIKCA and SAS CLUSTER, revealed that all three programs produce similar results In terms of hierarchical clustering, but NORMIX produces considerably more statistical evaluation and Information to the user. Thus NORMIX is recommended as the most useful cluster analysis program of these three.