Low-rank Decomposition Research Articles

ILN-SSR: Improved Logarithmic Norm and Sparse Structure Refinement for Infrared Small Target Detection

The effective discrimination of targets from backgrounds in environments characterized by a low signal-to-clutter ratio (SCR) is paramount for the advancement of infrared small target detection (IRSTD). In this work, we propose a novel detection framework predicated on low-rank sparse decomposition (LRSD), incorporating an improved logarithmic norm and a mechanism for sparse structure refinement, herein referred to as the improved logarithmic norm and sparse structure refinement (ILN-SSR). The ILN-SSR framework more precisely characterizes the sparse properties of both the background and the target, enabling a more effective distinction between the target and its background. Initially, our approach entails the utilization of an improved logarithmic norm to precisely estimate the low-rank attributes of the infrared image background. This is followed by the employment of a linear sparse regularization term alongside a target-traits-based sparse regularization term aimed at meticulously identifying targets within sparse regions and refining the sparse structure. Subsequently, we combine these components into the ILN-SSR framework, which formulates IRSTD as an optimization problem. The resolution of this framework is achieved through the implementation of the alternating direction method of multipliers (ADMM). The efficacy of the proposed framework is corroborated through the analysis of six image sequences. Comprehensive experimental assessments affirmed the framework’s substantial robustness in navigating various complex backgrounds.

X-ray coronary angiography background subtraction by adaptive weighted total variation regularized online RPCA

Objective.X-ray coronary angiograms (XCA) are widely used in diagnosing and treating cardiovascular diseases. Various structures with independent motion patterns in the background of XCA images and limitations in the dose of injected contrast agent have resulted in low-contrast XCA images. Background subtraction methods have been developed to enhance the visibility and contrast of coronary vessels in XCA sequences, consequently reducing the requirement for excessive contrast agent injections.Approach.The current study proposes an adaptive weighted total variation regularized online RPCA (WTV-ORPCA) method, which is a low-rank and sparse subspaces decomposition approach to subtract the background of XCA sequences. In the proposed method, the images undergo initial preprocessing using morphological operators to eliminate large-scale background structures and achieve image homogenization. Subsequently, the decomposition algorithm decomposes the preprocessed images into background and foreground subspaces. This step applies an adaptive weighted TV constraint to the foreground subspace to ensure the spatial coherency of the finally extracted coronary vessel images.Main results.To evaluate the effectiveness of the proposed background subtraction method, some qualitative and quantitative experiments are conducted on two clinical and synthetic low-contrast XCA datasets containing videos from 21 patients. The obtained results are compared with six state-of-the-art methods employing three different assessment criteria. By applying the proposed method to the clinical dataset, the mean values of the global contrast-to-noise ratio, local contrast-to-noise ratio, structural similarity index, and reconstruction error (RE) are obtained as5.976,3.173,0.987, and0.026, respectively. These criteria over the low-contrast synthetic dataset were4.851,2.942,0.958, and0.034, respectively.Significance.The findings demonstrate the superiority of the proposed method in improving the contrast and visibility of coronary vessels, preserving the integrity of the vessel structure, and minimizing REs without imposing excessive computational complexity.

Graph total variation and low-rank regularization for heterogeneous change detection

Heterogeneous change detection (HCD) is challenging because different imaging mechanisms for various sensors make images difficult to compare directly. To address this problem, a graph-based regression algorithm is proposed for HCD, by leveraging the Graph Total Variation regularization and Low-Rank matrices decomposition (GTVLR). Utilizing graph signal processing (GSP) theory, a directed graph (digraph) model is employed to effectively represent the orientation and correlation information of images, thereby enabling direct comparison of heterogeneous data within the same domain after graph filtering. The GTVLR framework facilitates the decomposition of post-event images into regression and changed images. This decomposition ensures that the regression image mirrors the structure similarity of the pre-event image, while the changed image highlights areas of alteration, aiding in change detection. The model characterizes the piecewise smoothness and Low-Rank properties of data through GTV regularization and Low-Rank penalty, respectively. Moreover, by integrating the higher-order neighboring information within the digraph to refine the model. Experiments conducted on three real-world datasets and comparison with several state-of-the-art methods demonstrate the effectiveness of the proposed algorithm.

Dual-grained Lightweight Strategy.

Removing redundant parameters and computations before the model training has attracted a great interest as it can effectively reduce the storage space of the model, speed up the training and inference of the model, and save energy consumption during the running of the model. In addition, the simplification of deep neural network models can enable high-performance network models to be deployed to resource-constrained edge devices, thus promoting the development of the intelligent world. However, current pruning at initialization methods exhibit poor performance at extreme sparsity. In order to improve the performance of the model under extreme sparsity, this paper proposes a dual-grained lightweight strategy-TEDEPR. This is the first time that TEDEPR has used tensor theory in the pruning at initialization method to optimize the structure of a sparse sub-network model and improve its performance. Specifically, firstly, at the coarse-grained level, we represent the weight matrix or weight tensor of the model as a low-rank tensor decomposition form and use multi-step chain operations to enhance the feature extraction capability of the base module to construct a low-rank compact network model. Secondly, unimportant weights are pruned at a fine-grained level based on the trainability of the weights in the low-rank model before the training of the model, resulting in the final compressed model. To evaluate the superiority of TEDEPR, we conducted extensive experiments on MNIST, UCF11, CIFAR-10, CIFAR-100, Tiny-ImageNet and ImageNet datasets with LeNet, LSTM, VGGNet, ResNet and Transformer architectures, and compared with state-of-the-art methods. The experimental results show that TEDEPR has higher accuracy, faster training and inference, and less storage space than other pruning at initialization methods under extreme sparsity.

Research on ECG signal reconstruction based on improved weighted nuclear norm minimization and approximate message passing algorithm.

In order to improve the energy efficiency of wearable devices, it is necessary to compress and reconstruct the collected electrocardiogram data. The compressed data may be mixed with noise during the transmission process. The denoising-based approximate message passing (AMP) algorithm performs well in reconstructing noisy signals, so the denoising-based AMP algorithm is introduced into electrocardiogram signal reconstruction. The weighted nuclear norm minimization algorithm (WNNM) uses the low-rank characteristics of similar signal blocks for denoising, and averages the signal blocks after low-rank decomposition to obtain the final denoised signal. However, under the influence of noise, there may be errors in searching for similar blocks, resulting in dissimilar signal blocks being grouped together, affecting the denoising effect. Based on this, this paper improves the WNNM algorithm and proposes to use weighted averaging instead of direct averaging for the signal blocks after low-rank decomposition in the denoising process, and validating its effectiveness on electrocardiogram signals. Experimental results demonstrate that the IWNNM-AMP algorithm achieves the best reconstruction performance under different compression ratios and noise conditions, obtaining the lowest PRD and RMSE values. Compared with the WNNM-AMP algorithm, the PRD value is reduced by 0.17∼4.56, the P-SNR value is improved by 0.12∼2.70.

Enhanced MRI brain tumor detection and classification via topological data analysis and low-rank tensor decomposition

The advent of artificial intelligence in medical imaging has paved the way for significant advancements in the diagnosis of brain tumors. This study presents a novel ensemble approach that uses magnetic resonance imaging (MRI) to identify and categorize common brain cancers, such as pituitary, meningioma, and glioma. The proposed workflow is composed of a two-fold approach: firstly, it employs non-trivial image enhancement techniques in data preprocessing, low-rank Tucker decomposition for dimensionality reduction, and machine learning (ML) classifiers to detect and predict the type of brain tumor. Secondly, persistent homology (PH), a topological data analysis (TDA) technique, is exploited to extract potential critical areas in MRI scans. When paired with the ML classifier output, this additional information can help domain experts to identify areas of interest that might contain tumor signatures, improving the interpretability of ML predictions. When compared to automated diagnoses, this transparency adds another level of confidence and is essential for clinical acceptance. The performance of the system was quantitatively evaluated on a well-known MRI dataset, with an overall classification accuracy of 97.28% using an extremely randomized trees model. The promising results show that the integration of TDA, ML, and low-rank approximation methods is a successful approach for brain tumor identification and categorization, providing a solid foundation for further study and clinical application.

Coastline target detection based on UAV hyperspectral remote sensing images

Timely and accurate monitoring of typical coastal targets using remote sensing technology is crucial for maintaining marine ecological stability. Hyperspectral target detection technology proves to be an effective tool in extracting various typical materials along the coastline. Traditional target detection methods using spectral domain information can effectively retain the intrinsic properties of the material. However, it is difficult to effectively recognize targets in homogeneous regions by using only spectral domain information, which may lead to insufficient utilization of spatial information. In this study, a detector based on signal-to-noise ratio fusion constrained energy minimization with low-rank sparse decomposition (SFLRSD) is proposed. This detector improves the separability of background and target by obtaining spatial domain information from hyperspectral images and fusing spectral domain information. First, total variation regularization and fractional Fourier transform are applied to process spatial and spectral domain information, respectively. The constrained energy minimization (CEM) detector is used to improve the separability between the target and background of the processed data. Then, the background and anomalies are represented as low-rank and sparse components, respectively, using low-rank sparse matrix factorization. This transforms the model solution into a covariance matrix problem, which is then solved using marginal distance difference (MDD) to isolate anomalous parts. Subsequently, the anomaly parts are fused with CEM detector results, weighted by their respective signal-to-noise ratios. This detection model leverages unified hyperspectral image features, enhancing spectral discreteness of anomalous targets and backgrounds. Finally, experiments on custom created hyperspectral dataset show that the proposed method outperforms other baseline methods in terms of visualization and quantitative performance. In this paper, we not only propose a new hyperspectral target detection method, but we also collect three typical marine litter of different materials by means of airborne hyperspectral remote sensing and construct four hyperspectral datasets in a real environment. All the simulation experiments in this paper are conducted in these four datasets.

Finite-frequency model order reduction of linear and bilinear systems via low-rank approximation

In this paper, we first investigate the finite-frequency model order reduction for linear systems based on low-rank Gramian approximations. An efficient algorithm for computing low-rank approximations of the finite-frequency and frequency-dependent Gramians based on Laguerre functions is proposed. The approach constructs the low-rank decomposition factors of the finite-frequency Gramians or frequency-dependent Gramians through a recursive formula of Laguerre functions expansion coefficient vectors and then combines the low-rank square root method and frequency-dependent balanced truncation method to obtain the reduced-order models. In this process, it avoids dealing with the matrix-valued functions and solving the related (generalized) Lyapunov matrix equations directly, making them computationally efficient. Furthermore, the above method is successfully extended to bilinear systems, and a corresponding efficient computation method for low-rank approximations of the finite-frequency Gramians of bilinear systems is derived. Finally, some numerical simulations are provided to illustrate the effectiveness of our proposed algorithms.

Low-Rank Robust Subspace Tensor Clustering for Metro Passenger Flow Modeling

Tensor clustering has become an important topic, specifically in spatiotemporal modeling, because of its ability to cluster spatial modes (e.g., stations or road segments) and temporal modes (e.g., time of day or day of the week). Our motivating example is from subway passenger flow modeling, where similarities between stations are commonly found. However, the challenges lie in the innate high-dimensionality of tensors and also the potential existence of anomalies. This is because the three tasks, that is, dimension reduction, clustering, and anomaly decomposition, are intercorrelated with each other, and treating them in a separate manner will render a suboptimal performance. Thus, in this work, we design a tensor-based subspace clustering and anomaly decomposition technique for simultaneous outlier-robust dimension reduction and clustering for high-dimensional tensors. To achieve this, a novel low-rank robust subspace clustering decomposition model is proposed by combining Tucker decomposition, sparse anomaly decomposition, and subspace clustering. An effective algorithm based on Block Coordinate Descent is proposed to update the parameters. Prudent experiments prove the effectiveness of the proposed framework via the simulation study, with a gain of +25% clustering accuracy over benchmark methods in a hard case. The interrelations of the three tasks are also analyzed via ablation studies, validating the interrelation assumption. Moreover, a case study in station clustering based on real passenger flow data is conducted, with quite valuable insights discovered. History: Bianca Maria Colosimo served as the senior editor for this article. Funding: Dr. Yan is partially funded by DOE [DE-EE0009354] and NSF [CMMI 2316654]. Dr. Fugee is partially funded with the RGC [GRF 16201718 and 16216119]. The authors appreciate the help from the Hong Kong MTR Co. research, marketing, and customer service teams. Data Ethics & Reproducibility Note: The code capsule is available on Code Ocean at https://codeocean.com/capsule/6536164/tree and in the e-Companion to this article (available at https://doi.org/10.1287/ijds.2022.0028 ).

Enhanced Low-Rank Matrix Decomposition for High-Resolution UAV-SAR Imagery

Enhanced Low-Rank Matrix Decomposition for High-Resolution UAV-SAR Imagery

A robust underwater polarization image recovery based on Angle of Polarization with low-rank and sparse decomposition

Underwater imaging method based on the Angle of Polarization (AoP) is extremely popular due to its ability to remove the backscattered light effectively. However, existing methods overlook a potentially important phenomenon: the AoP contains significant noise in the real world, which leads to inaccurate estimations of key parameters. In this study, we propose a novel robust underwater polarization image recovery method based on AoP with low-rank and sparse decomposition. Based on the analysis of polarization, the AoP of backscattering exhibits low-rank characteristics, whereas the AoP of noise and targets demonstrates sparsity. Considering different sparsity of AoP, we combine Robust Principal Component Analysis and Alternating Direction Multiplier Method (RPCA-ADMM) with an adaptive threshold shrinkage method for low-rank and sparse decomposition, the AoP of the backscattering is obtained. Moreover, according to the low-rank component of the AoP, the Degree of Linear Polarization (DoLP) of backscattering can be effectively and automatically estimated without considering whether the background region exists, relying on a frequency prior strategy. Finally, the degraded image is recovered utilizing underwater polarization imaging model. Extensive experimental results demonstrate that the recovered images from the proposed method have abundant detail, high contrast, and minimal color distortion, which is competitive with most state-of-the-art methods.

ConDiff-rPPG: Robust Remote Physiological Measurement to Heterogeneous Occlusions.

Remote photoplethysmography (rPPG) is a contactless technique that facilitates the measurement of physiological signals and cardiac activities through facial video recordings. This approach holds tremendous potential for various applications. However, existing rPPG methods often did not account for different types of occlusions that commonly occur in real-world scenarios, such as temporary movement or actions of humans in videos or dust on camera. The failure to address these occlusions can compromise the accuracy of rPPG algorithms. To address this issue, we proposed a novel Condiff-rPPG to improve the robustness of rPPG measurement facing various occlusions. First, we compressed the damaged face video into a spatio-temporal representation with several types of masks. Second, the diffusion model was designed to recover the missing information with observed values as a condition. Moreover, a novel low-rank decomposition regularization was proposed to eliminate background noise and maximize informative features. ConDiff-rPPG ensured optimization goal consistency during the training process. Through extensive experiments, including intra- and cross-dataset evaluations, as well as ablation tests, we demonstrated the robustness and generalization ability of our proposed model.

Ptycho-endoscopy on a lensless ultrathin fiber bundle tip

Synthetic aperture radar (SAR) utilizes an aircraft-carried antenna to emit electromagnetic pulses and detect the returning echoes. As the aircraft travels across a designated area, it synthesizes a large virtual aperture to improve image resolution. Inspired by SAR, we introduce synthetic aperture ptycho-endoscopy (SAPE) for micro-endoscopic imaging beyond the diffraction limit. SAPE operates by hand-holding a lensless fiber bundle tip to record coherent diffraction patterns from specimens. The fiber cores at the distal tip modulate the diffracted wavefield within a confined area, emulating the role of the ‘airborne antenna’ in SAR. The handheld operation introduces positional shifts to the tip, analogous to the aircraft’s movement. These shifts facilitate the acquisition of a ptychogram and synthesize a large virtual aperture extending beyond the bundle’s physical limit. We mitigate the influences of hand motion and fiber bending through a low-rank spatiotemporal decomposition of the bundle’s modulation profile. Our tests demonstrate the ability to resolve a 548-nm linewidth on a resolution target. The achieved space-bandwidth product is ~1.1 million effective pixels, representing a 36-fold increase compared to that of the original fiber bundle. Furthermore, SAPE’s refocusing capability enables imaging over an extended depth of field exceeding 2 cm. The aperture synthesizing process in SAPE surpasses the diffraction limit set by the probe’s maximum collection angle, opening new opportunities for both fiber-based and distal-chip endoscopy in applications such as medical diagnostics and industrial inspection.

Shallow sea reverberation suppression based on a range azimuth patch matrix model.

Reverberation is the main background interference for active sonar detection in shallow sea. Reverberation suppression is crucial for enhancing the performance of active sonar. In this paper, a reverberation suppression method based on low-rank sparse decomposition is proposed. First, both the sparseness property of the targets and the non-local self-correlation property of the reverberation are used to construct a range azimuth patch matrix model. The reverberation suppression problem is then transformed into an optimization problem for the recovery of a low-rank sparse matrix. The validity of the proposed method is verified by using the measured data. Results show that, compared with the reverberation pre-whitening and sparse fractional Fourier transform methods, the proposed method significantly improves the reverberation suppression performance and achieves a better detection result when the signal-to-interference ratio is below -2 dB.

Bound-state stability of Coulomb three-body systems using numerical tensor methods

In this paper we present a unified treatment of three-body atoms and molecules using numerical tensor methods. The Schrödinger equation in perimetric coordinates is recast in a canonical tensor format. It is shown that the Schrödinger equation can be solved in this full-tensor format but that by using a low-rank tensor decomposition, in particular the tensor-train and quantized-tensor-train formats, energies accurate to at least the nanohartree can be obtained for the He atom (in which the mass of the uniquely charged particle is much greater than the other two particles), the positronium negative ion (Ps−, in which all the masses are equal), and the non-Born-Oppenheimer H2+ molecule (in which the mass of the uniquely charged particle is much smaller than the other two particles). Published by the American Physical Society 2024

A non-convex low-rank image decomposition model via unsupervised network

Image decomposition is the separation of a given image into two parts with different features, i.e., structure and texture. In order to extract the image information comprehensively, a non-convex unsupervised image decomposition model is proposed in this paper. Firstly, we propose a new non-convex low-rank regular term to describe the low-rank nature of images, which focuses on optimizing the sum of partial singular values of image matrices using a non-convex truncated nuclear norm. Secondly, unsupervised network is used to capture image information by learning the deep semantic information of the image and then extracting the image structure. Finally, the alternative direction method of multipliers is used to divide the model into three sub-problems and optimize them separately. For the non-convex sub-problem, a two-stage solution scheme is given by employing the singular value decomposition technique, and experimental analysis is carried out on both real and synthetic images. The experimental results show that the proposed non-convex image decomposition method outperforms other state-of-the-art methods in terms of subjective visual effects. Meanwhile, in the quantitative evaluation, the proposed method shows a large improvement compared with other methods, with a maximum improvement of 15 % in the structural similarity index measure (SSIM) index.

Robust PCA with Lw,∗ and L2,1 Norms: A Novel Method for Low-Quality Retinal Image Enhancement.

Nonmydriatic retinal fundus images often suffer from quality issues and artifacts due to ocular or systemic comorbidities, leading to potential inaccuracies in clinical diagnoses. In recent times, deep learning methods have been widely employed to improve retinal image quality. However, these methods often require large datasets and lack robustness in clinical settings. Conversely, the inherent stability and adaptability of traditional unsupervised learning methods, coupled with their reduced reliance on extensive data, render them more suitable for real-world clinical applications, particularly in the limited data context of high noise levels or a significant presence of artifacts. However, existing unsupervised learning methods encounter challenges such as sensitivity to noise and outliers, reliance on assumptions like cluster shapes, and difficulties with scalability and interpretability, particularly when utilized for retinal image enhancement. To tackle these challenges, we propose a novel robust PCA (RPCA) method with low-rank sparse decomposition that also integrates affine transformations τi, weighted nuclear norm, and the L2,1 norms, aiming to overcome existing method limitations and to achieve image quality improvement unseen by these methods. We employ the weighted nuclear norm (Lw,∗) to assign weights to singular values to each retinal images and utilize the L2,1 norm to eliminate correlated samples and outliers in the retinal images. Moreover, τi is employed to enhance retinal image alignment, making the new method more robust to variations, outliers, noise, and image blurring. The Alternating Direction Method of Multipliers (ADMM) method is used to optimally determine parameters, including τi, by solving an optimization problem. Each parameter is addressed separately, harnessing the benefits of ADMM. Our method introduces a novel parameter update approach and significantly improves retinal image quality, detecting cataracts, and diabetic retinopathy. Simulation results confirm our method's superiority over existing state-of-the-art methods across various datasets.

Tensor low-rank and sparse decomposition and its application in bearing fault information separation

Abstract Properly separating fault information from noisy measured signals is crucial for effective bearing health sensing. However, conventional fault information separation methods face challenges such as predefined model parameters and poor noise robustness. Additionally, with the advent of Industry Big Data, multichannel monitoring signals present significant challenges for traditional single decomposition approaches. To address these challenges and fully extract potential fault information, this paper introduces a tensor low-rank and sparse decomposition (tensor LRSD) approach for multichannel signal processing. Inspired by matrix LRSD, we construct a tensor LRSD model that adaptively decomposes the signal into a tensor sparse term containing fault information and a low-rank term representing the intrinsic signal pattern. To further enhance the decomposition performance, a maximum correlation-based selection strategy is designed. This strategy evaluates the correlation between each tensor slice and selects appropriate tensor sparse terms for fault information extraction. Simulation analysis and two experimental studies involving typical bearing failures are implemented to verify the capability and superiority of the presented tensor LRSD approach. The consequences demonstrate that the presented method outperforms conventional techniques, showcasing its capability to effectively separate fault information from noisy signals.

A novel image hashing with low-rank sparse matrix decomposition and feature distance

A novel image hashing with low-rank sparse matrix decomposition and feature distance

Novel Deep Learning Domain Adaptation Approach for Object Detection Using Semi-Self Building Dataset and Modified YOLOv4

Moving object detection is a vital research area that plays an essential role in intelligent transportation systems (ITSs) and various applications in computer vision. Recently, researchers have utilized convolutional neural networks (CNNs) to develop new techniques in object detection and recognition. However, with the increasing number of machine learning strategies used for object detection, there has been a growing need for large datasets with accurate ground truth used for the training, usually demanding their manual labeling. Moreover, most of these deep strategies are supervised and only applicable for specific scenes with large computational resources needed. Alternatively, other object detection techniques such as classical background subtraction need low computational resources and can be used with general scenes. In this paper, we propose a new a reliable semi-automatic method that combines a modified version of the detection-based CNN You Only Look Once V4 (YOLOv4) technique and background subtraction technique to perform an unsupervised object detection for surveillance videos. In this proposed strategy, background subtraction-based low-rank decomposition is applied firstly to extract the moving objects. Then, a clustering method is adopted to refine the background subtraction (BS) result. Finally, the refined results are used to fine-tune the modified YOLO v4 before using it in the detection and classification of objects. The main contribution of this work is a new detection framework that overcomes manual labeling and creates an automatic labeler that can replace manual labeling using motion information to supply labeled training data (background and foreground) directly from the detection video. Extensive experiments using real-world object monitoring benchmarks indicate that the suggested framework obtains a considerable increase in mAP compared to state-of-the-art results on both the CDnet 2014 and UA-DETRAC datasets.