Low-rank Decomposition Method Research Articles

Fractional-order velocity-dilatation-rotation viscoelastic wave equation and numerical solution based on a constant-Q model

Viscoelastic wave equations based on the constant- Q (CQ) model can accurately describe the amplitude dissipation and phase distortion of waves in anelastic media. However, only three velocity or displacement components can be obtained directly by solving such equations. Starting from the time-domain second-order displacement viscoelastic wave equation, we derived the decoupled P- and S-wave displacement vector viscoelastic wave equation by using the polarization difference of P- and S-wave propagation in isotropic media. The equation can be transformed into the velocity-dilatation-rotation viscoelastic wave equation containing the first-order temporal derivative and fractional Laplacian operators, which can be solved directly by using the staggered-grid finite-difference and pseudospectral methods. We use the low-rank decomposition method to approximate the derived mixed space-wavenumber domain fractional Laplacian operators for modeling wave propagation in heterogeneous attenuating media. We also demonstrated the precision of our equation by comparing the numerical solutions with the analytical solutions. Furthermore, compared with the conventional velocity-stress viscoelastic wave equation, experimental results demonstrate that our equation can separate the pure P and S waves from the mixed wavefield during wavefield continuation. In addition, it can be separated into an equation containing predominantly an amplitude attenuation or a phase distortion term.

A federated distillation domain generalization framework for machinery fault diagnosis with data privacy

Federated learning is an emerging technology that enables multiple clients to cooperatively train an intelligent diagnostic model while preserving data privacy. However, federated diagnostic models still suffer from a performance drop when applied to entirely unseen clients outside the federation in practical deployments. To address this issue, a Federated Distillation Domain Generalization (FDDG) framework is proposed for machinery fault diagnosis. The core idea is to enable individual clients to access multi-client data distributions in a privacy-preserving manner and further explore domain invariance to enhance model generalization. A novel diagnostic knowledge-sharing mechanism is designed based on knowledge distillation, which equips multiple generators to augment fake data during the training of local models. Based on generated data and real data, a low-rank decomposition method is utilized to mine domain invariance, enhancing the model's ability to resist domain shift. Extensive experiments on two rotating machines demonstrate that the proposed FDDG achieves a 3% improvement in accuracy compared to state-of-the-art methods.

Frequency-dependent Q simulation and viscoacoustic reverse time migration based on the fractional Zener model

Seismic attenuation is a basic physical property of the earth, which significantly affects the characteristics of seismic wavefields. Accurately simulating wave propagation in the earth is essential to image subsurface structures. Some prevailing methods (e.g., the standard linear solid and fractional Laplacian equation) to describe seismic wave propagation in attenuating media are mainly based on the constant- Q model (CQM), which is valid at room temperature and pressure. However, laboratory measurements suggest that the quality factor Q is a function of frequencies in some regions. To simulate the frequency-dependent Q effect, we derive a viscoacoustic wave equation from the stress-strain relationship of the fractional Zener model (FZM) with variable fractional orders. During the implementation, we separate the real and imaginary parts of the modulus and introduce a low-rank decomposition method to solve the FZM equation. Because the amplitude dissipation and phase dispersion are decoupled, we establish a compensated reverse time migration ( Q-RTM) algorithm to mitigate adverse effects caused by seismic attenuation and improve the quality of seismic migration in frequency-dependent attenuating media. A two-layer model and the BP gas chimney model are used to perform Q-RTM tests. A low-pass filter with a Tukey window function is applied to suppress numerical instability during the compensation. Numerical results demonstrate that our FZM Q-RTM approach can produce high-resolution images with corrected reflector positions and amplitudes. Because the CQM equation ignores the frequency dependence of Q, it may lead to overcompensation in Q-RTM.

A survey of model compression strategies for object detection

Deep neural networks (DNNs) have achieved great success in many object detection tasks. However, such DNNS-based large object detection models are generally computationally expensive and memory intensive. It is difficult to deploy them to devices with low memory resources or scenarios with high real-time requirements, which greatly limits their application and promotion. In recent years, many researchers have focused on compressing large object detection models without significantly degrading their performance, and have made great progress. Therefore, this paper presents a survey of object detection model compression techniques in recent years. Firstly, these compression techniques were divided into six categories: network pruning, lightweight network design, neural architecture search (NAS), low-rank decomposition, network quantization, and Knowledge distillation (KD) methods. For each category, we select some representative state-of-the-art methods and compare and analyze their performance on public datasets. After that, we discuss the application scenarios and future directions of model compression techniques. Finally, this paper is further concluded by analyzing the advantages and disadvantages of six types of model compression techniques.

Video SAR Moving Target Shadow Detection Based on Intensity Information and Neighborhood Similarity

Video Synthetic Aperture Radar (SAR) has shown great potential in moving target detection and tracking. At present, most of the existing detection methods focus on the intensity information of the moving target shadow. According to the mechanism of shadow formation, some shadows of moving targets present low contrast, and their boundaries are blurred. Additionally, some objects with low reflectivity show similar features with them. These cause the performance of these methods to degrade. To solve this problem, this paper proposes a new moving target shadow detection method, which consists of background modeling and shadow detection based on intensity information and neighborhood similarity (BIIANS). Firstly, in order to improve the efficiency of image sequence generation, a fast method based on the Back-projection imaging algorithm (f-BP) is proposed. Secondly, due to the low-rank characteristics of stationary objects and the sparsity characteristics of moving target shadows presented in the image sequence, this paper introduces the low-rank sparse decomposition (LRSD) method to perform background modeling for obtaining better background (static objects) and foreground (moving targets) images. Because the shadows of moving targets appear in the same position in the original and the corresponding foreground images, the similarity between them is high and independent of their intensity. Therefore, using the BIIANS method can obtain better shadow detection results. Real W-band data are used to verify the proposed method. The experimental results reveal that the proposed method performs better than the classical methods in suppressing false alarms, missing alarms, and improving integrity.

Accurate Multiobjective Low-Rank and Sparse Model for Hyperspectral Image Denoising Method

Due to the unavoidable influence of sparse and Gaussian noise during the process of data acquisition, the quality of hyperspectral images (HSIs) is degraded and their applications are greatly limited. It is therefore necessary to restore clean HSIs. In the traditional methods, low-rank and sparse matrix decomposition methods are usually applied to restore the pure data matrix from the observed data matrix. However, due to the fact that the optimization of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${l}_{0}$ </tex-math></inline-formula> -norm for the sparse modeling is a nonconvex and NP-hard problem, convex relaxation and regularization parameters are usually introduced. However, convex relaxation often leads to inaccurate sparse modeling results, and the sensitive regularization parameters can lead to unstable results. Thus, in this article, to address these issues, an accurate multiobjective low-rank and sparse denoising framework is proposed for HSIs to achieve accurate modeling. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${l}_{0}$ </tex-math></inline-formula> -norm is directly modeled as the sparse noise and is optimized by an evolutionary algorithm, and the denoising problem is converted into a multiobjective optimization problem through simultaneously optimizing the low-rank term, the sparse term, and the data fidelity term, without sensitive regularization parameters. However, since the low-rank clean image and sparse noise of the HSI are encoded into a solution, the length of the solution is too long to be optimized. In this article, a subfitness strategy is constructed to achieve effective optimization by comparing the objective function values corresponding to each band for each solution. The experiments undertaken with simulated images in 11 noise cases and four real noisy images confirm the effectiveness of the proposed method.

Learning Dual Low-Rank Representation for Multi-Label Micro-Video Classification

Currently, with the rapid development of mobile Internet, micro-video has become a prevailing format of user-generated contents (UGCs) on various social media platforms. Several studies have been conducted towards to understanding high-level micro-video semantics, such as venue categorization, memorability, and popularity. However, these approaches supported tasks with only a single output, which exhibited limitations when attempting to use them to resolve tasks with multiple outputs, especially the multi-label micro-video classification. To tackle this problem, in this paper, we propose a dual multi-modal low-rank decomposition (DMLRD) method for multi-label micro-video classification tasks. To learn more comprehensive micro-video representations, we first learn the low-rank-regularized modality-specific and modality-shared components by considering the consistency and the complementarity among modalities simultaneously. Meanwhile, the less descriptive power of each modality aroused by inherent properties can be solved to a certain extent. To obtain unseen label representations, we next construct a sparsity-regularized multi-matrix normal estimation term to jointly encode the latent relationship structures among labels and dimensions. Experiments on two datasets demonstrate the effectiveness of our proposed method over the state-of-art methods.

Streaming Data Preprocessing via Online Tensor Recovery for Large Environmental Sensor Networks

Measuring the built and natural environment at a fine-grained scale is now possible with low-cost urban environmental sensor networks. However, fine-grained city-scale data analysis is complicated by tedious data cleaning including removing outliers and imputing missing data. While many methods exist to automatically correct anomalies and impute missing entries, challenges still exist on data with large spatial-temporal scales and shifting patterns. To address these challenges, we propose an online robust tensor recovery (OLRTR) method to preprocess streaming high-dimensional urban environmental datasets. A small-sized dictionary that captures the underlying patterns of the data is computed and constantly updated with new data. OLRTR enables online recovery for large-scale sensor networks that provide continuous data streams, with a lower computational memory usage compared to offline batch counterparts. In addition, we formulate the objective function so that OLRTR can detect structured outliers, such as faulty readings over a long period of time. We validate OLRTR on a synthetically degraded National Oceanic and Atmospheric Administration temperature dataset, and apply it to the Array of Things city-scale sensor network in Chicago, IL, showing superior results compared with several established online and batch-based low-rank decomposition methods.

A sparse and spectral smooth regularized low-rank tensor decomposition method for hyperspectral target detection

ABSTRACT In recent years, hyperspectral target detection methods have been widely used in military or civilian fields. Many high-performance hyperspectral target detection methods have been proposed, and tensor decomposition-based methods have attracted the attention of researchers. However, the non-uniqueness of tensor rank and the interference of noise will reduce the effect of target detection. In order to solve these problems, a sparse and spectral smooth regularized low-rank tensor decomposition method for hyperspectral target detection is proposed in this paper. The proposed method adds the low-rank regularization to the factor matrix of the tensor decomposition framework, which can reduce the adverse effect of information redundancy on the detection effect of the algorithm. Furthermore, the spectral smooth regularization is added to the spectral factor matrix to suppress noise and the sparse regularization is added to the core tensor to solve the problems of non-uniqueness of the Tucker tensor decomposition, which can improve the effect of target detection. On this basis, it simplifies the calculation process and reduces the complexity of the algorithm by using the conjugate gradient algorithm and the tensor Kronecker product. In this paper, the algorithm is tested on four real hyperspectral data sets and compared with six state-of-the-art algorithms. The experimental results show that targets detected by the proposed method are more obvious and the background is more pure.

Robust shallow water reverberation reduction methods based on low-rank and sparsity decomposition.

Using the characteristics of low rank for reverberation and sparsity for the target echo in multi-ping detection, the low-rank and sparsity decomposition method can effectively reduce reverberation. However, in the case of highly sparse reverberation or a stationary target, the distinctions in the characteristics between the reverberation and target echo become ambiguous. As a result, the reverberation reduction performance is degraded. To guarantee a meaningful decomposition based on the random orthogonal model and random sparsity model, the identifiability condition (IC) for the decomposition was derived from the perspective of the low-rank matrix and sparse matrix, respectively. According to the IC, sparsity compensation for the low-rank matrix was proposed to address the false alarm probability inflation (FAPI) induced by highly sparse reverberation. In addition, increasing the dimension of the sparse matrix was also proposed to manage the detection probability shrinkage caused by a stationary target. The robust reverberation reduction performance was validated via simulations and field experiments. It is demonstrated that FAPI can be eliminated by increasing the sparse coefficient of the low-rank matrix to 0.30 and a stationary target could be detected with a large ping number, i.e., a high dimension, of the sparse matrix.

Online quality inspection of resistance spot welding for automotive production lines

Reliable quality control of resistance spot welding (RSW) is a long-standing challenge, due to random disturbance on automotive production lines. In this paper, a quality evaluation framework is proposed based on dynamic resistance (DR) signals, aiming to accurately predict welding quality. The proposed framework integrates welding process stability with deep learning models. Given the uniform variation pattern of each weld with the same schedule, process stability can be determined based on the reference curve constructed by the low-rank and sparse decomposition method. Subsequently, a one-dimensional convolutional neural network (1DCNN) with channel attention mechanism is developed to further predict welding quality, which can perform channel-wise feature recalibration to enhance the classification performance. Extensive experiments substantiate that the proposed network yields a remarkable classification performance compared with typical algorithms on several RSW datasets collected on an actual production line. This study provides a valuable reference to achieve an intelligent online quality inspection system in the automotive manufacturing industry.

Infrared Small Target Detection Algorithm Based on Local Spatial Gradient Peak

A sparse infrared small target detection algorithm based on local spatial gradient peaks is proposed to deal with the problem of slow running speed and edge sensitivity in low-rank decomposition methods.The detection steps are as follows. In the first step, the image expansion operation is used for preprocessing. We use the circular structure element to sharpen the edges of targets and smooth the background noise. Then, the saliency gradient features of the target local region are applied to calculate the overlapping gradient information of the image after expansion. The local area with a larger gradient peak is located in the original image, and the selected local area is considered to be the region of interest with candidate targets. Finally, we use the advanced accelerated proximal gradient algorithm to perform matrix decomposition in the extracted local regions of interest to extract sparse infrared small targets. Extensive experimental results under real scenarios illustrated that compared with the baseline low-rank sparse decomposition method, the proposed approach runs faster and shows superior detection performance in the comprehensive evaluation index.

Declutter-GAN: GPR B-Scan Data Clutter Removal Using Conditional Generative Adversarial Nets

Clutter removal in ground-penetrating radar (GPR) B-scan data has been widely studied in recent years. In this letter, we propose a novel data-driven clutter suppression method in GPR data based on conditional generative adversarial nets (cGANs). The proposed method learns a function that maps the cluttered data to the clutter-free data from the training set. The training set consists of pairs of cluttered data and corresponding clutter-free data. Different from the traditional method that only uses the simulation training set, we simulate the clutter-free data and add the real collected non-target data to the simulated clutter-free data as cluttered data, so that the trained network can generalize well to the real GPR data. The proposed method is compared with the subspace method, sparse representation-based method, and low-rank and sparse matrix decomposition (LRSD) methods on both simulation data and real collected data. The results show that the proposed method has higher performance in terms of computational complexity, clutter suppression results, and applicability than those state-of-the-art methods.

GPR Clutter Removal Based on Factor Group-Sparse Regularization

Clutter removal is of vital importance to underground detection via ground penetrating radar (GPR) since the target response is usually overwhelmed by strong clutter. The low-rank and sparse decomposition (LRSD) method, which decomposes the GPR data into a low-rank background matrix and a sparse target matrix, has been applied in GPR. However, the existing LRSD-based methods, such as robust principal component analysis (RPCA) and robust non-negative matrix factorization, are sensitive to the regularization parameter or have high computation complexity. In this letter, a novel clutter removal based on factor group-sparse regularization is proposed. It uses a nonconvex matrix factorization as a surrogate for the matrix rank rather than the nuclear norm as in the RPCA. It has good efficiency and robustness to the parameters. Simulation and experimental results demonstrate that the proposed method has higher performance in terms of the improvement factor values and lower computational complexity than the state-of-the-art methods.

A Novel Convolutional Autoencoder-Based Clutter Removal Method for Buried Threat Detection in Ground-Penetrating Radar

The clutter encountered in ground-penetrating radar (GPR) systems seriously affects the performance of the subsurface target detection methods. A new clutter removal method based on convolutional autoencoders (CAEs) is introduced. The raw GPR image is encoded via successive convolution and pooling layers and then decoded to provide the clutter-free GPR image. The loss function is defined in terms of the reference clutter-free target image and the decoder output is optimized to learn the weight coefficients from the raw data. The method is compared to the conventional subspace methods, recently proposed nonnegative matrix factorization, as well as low-rank and sparse decomposition (LRSD) methods and dictionary separation-based morphological component analysis. CAE and its deeper version deep CAE (DCAE) are trained by several scenarios generated by the electromagnetic simulation tool gprMax. Simulation results demonstrate the effectiveness of the proposed method for challenging scenarios. While for real GPR image, the simulated data trained networks remain slightly behind the LRSD methods for the dry case, nonetheless, they outperform the aforementioned processing techniques for the more challenging wet case.

Single-Channel Circular SAR Ground Moving Target Detection Based on LRSD and Adaptive Threshold Detector

Due to the advantages of long-time and multi-angle observation, ground moving target detection with circular synthetic aperture radar (SAR) has recently attracted lots of interest from researchers. Our team has previously proposed the logarithm background subtraction algorithm for moving target detection in single-channel circular SAR. Its principle is that the background image (static clutter) is obtained by median filtering of the image sequence, and the foreground image (moving target) is obtained by subtraction. To further improve the performance of background and foreground separation, we introduce the low-rank sparse decomposition (LRSD) method into the previous framework. A new algorithm based on LRSD and adaptive threshold detector (ATD) is proposed in this letter. First, this letter introduces entropy metric to optimize parameters in LRSD to obtain better background and foreground separation. Second, since the statistical distribution of the foreground image is unknown, the constant false alarm rate (CFAR) detector cannot be applied to the foreground image. Therefore, an adaptive threshold detector (ATD) built on Otsu is presented in this letter, which is independent of image statistical properties. The final detection result is obtained via clustering using the modified density-based spatial clustering of applications with noise (DBSCAN) method. The effectiveness of the proposed algorithm is verified by the experimental results on the airborne X-band Gotcha Volumetric SAR Data.

Joint reconstruction and low-rank decomposition for dynamic inverse problems

&lt;p style='text-indent:20px;'&gt;A primary interest in dynamic inverse problems is to identify the underlying temporal behaviour of the system from outside measurements. In this work, we consider the case, where the target can be represented by a decomposition of spatial and temporal basis functions and hence can be efficiently represented by a low-rank decomposition. We then propose a joint reconstruction and low-rank decomposition method based on the Nonnegative Matrix Factorisation to obtain the unknown from highly undersampled dynamic measurement data. The proposed framework allows for flexible incorporation of separate regularisers for spatial and temporal features. For the special case of a stationary operator, we can effectively use the decomposition to reduce the computational complexity and obtain a substantial speed-up. The proposed methods are evaluated for three simulated phantoms and we compare the obtained results to a separate low-rank reconstruction and subsequent decomposition approach based on the widely used principal component analysis.&lt;/p&gt;

Double sparse low rank decomposition for irregular printed fabric defect detection

In this paper, a double sparse low-rank decomposition method is proposed to defect detection for complex irregular printed fabrics. Firstly, a low rank decomposition model with double sparsity is established by taking the sparse components as the printing template prior and the difference between the defective printed fabric graph and the template fabric graph as the defect prior. Secondly, the decomposition is guided by printing prior and defect for the double sparse low rank decomposition model to obtain the saliency map of defects. Furthermore, the defect map is obtained by binarising the defect’s saliency map using the optimal threshold segmentation. Finally, the simulation results are compared with the four existing methods. The results show that the proposed algorithm can effectively detect defects in three types of irregular printed fabrics, such as small-size print, medium-size print, and complex-distribution print. The valid positive rate is 89.29%, the false positive rate is 0.85%, and the positive predictive value is 86.21%. Comparison results show that the proposed algorithm retains the shape details of the defect better than the other four algorithms, and the detection time is 12.49% less than the current optimal PN-RPCA algorithm.

Hyperspectral Super-Resolution Via Joint Regularization of Low-Rank Tensor Decomposition

The hyperspectral image super-resolution (HSI-SR) problem aims at reconstructing the high resolution spatial–spectral information of the scene by fusing low-resolution hyperspectral images (LR-HSI) and the corresponding high-resolution multispectral image (HR-MSI). In order to effectively preserve the spatial and spectral structure of hyperspectral images, a new joint regularized low-rank tensor decomposition method (JRLTD) is proposed for HSI-SR. This model alleviates the problem that the traditional HSI-SR method, based on tensor decomposition, fails to adequately take into account the manifold structure of high-dimensional HR-HSI and is sensitive to outliers and noise. The model first operates on the hyperspectral data using the classical Tucker decomposition to transform the hyperspectral data into the form of a three-mode dictionary multiplied by the core tensor, after which the graph regularization and unidirectional total variational (TV) regularization are introduced to constrain the three-mode dictionary. In addition, we impose the l1-norm on core tensor to characterize the sparsity. While effectively preserving the spatial and spectral structures in the fused hyperspectral images, the presence of anomalous noise values in the images is reduced. In this paper, the hyperspectral image super-resolution problem is transformed into a joint regularization optimization problem based on tensor decomposition and solved by a hybrid framework between the alternating direction multiplier method (ADMM) and the proximal alternate optimization (PAO) algorithm. Experimental results conducted on two benchmark datasets and one real dataset show that JRLTD shows superior performance over state-of-the-art hyperspectral super-resolution algorithms.

Vector elastic deconvolution migration with dual wavefield decomposition

Elastic-wave imaging using multicomponent data can provide more useful subsurface information than acoustic-wave imaging, but it is usually algorithmically challenging. We have developed a vector elastic deconvolution migration method for high-resolution imaging of subsurface structures in isotropic and anisotropic elastic media. Our new method uses a vector deconvolution imaging condition based on dual wavefield decomposition, including an explicit directional wavefield separation using the Hilbert transform and a P/S vector wavefield decomposition using the low-rank decomposition method. Using three elastic models, we numerically determine that our new method produces notably higher resolution and more amplitude-balanced elastic images compared with a crosscorrelation-based vector elastic reverse time migration method.