Sparse Representation Algorithm Research Articles

A multi-dictionary fusion method based on improved dynamic time warping for moveable rail damage localization

Abstract Traditional structural health monitoring (SHM) of rails relies on a fixed single sensor, limited by detection range and noise interference. Therefore, a multi-dictionary fusion method for movable rail damage localization is proposed based on improved dynamic time warping (DTW). The approach combines onboard acoustic emission sensors with peak detection frames to measure the moving distance of the inspection wheels and monitor a wide range of rails. Aiming to enhance the damage information, an innovative DTW-based multi-dictionary sparse representation algorithm is presented for data fusion. The second-order difference of the Mahalanobis distance is employed to optimize the fusion weights from the global property. A two-feature adaptive threshold is designed to precisely detect and localize damage on rails. The effectiveness of this method is verified at laboratory testing speeds less than 0.75 m s−1. The results demonstrate that it can accurately detect 2 mm deep strip and square damage, providing new inspiration for rail SHM.

Sparse representation for restoring images by exploiting topological structure of graph of patches

AbstractImage restoration poses a significant challenge, aiming to accurately recover damaged images by delving into their inherent characteristics. Various models and algorithms have been explored by researchers to address different types of image distortions, including sparse representation, grouped sparse representation, and low‐rank self‐representation. The grouped sparse representation algorithm leverages the prior knowledge of non‐local self‐similarity and imposes sparsity constraints to maintain texture information within images. To further exploit the intrinsic properties of images, this study proposes a novel low‐rank representation‐guided grouped sparse representation image restoration algorithm. This algorithm integrates self‐representation models and trace optimization techniques to effectively preserve the original image structure, thereby enhancing image restoration performance while retaining the original texture and structural information. The proposed method was evaluated on image denoising and deblocking tasks across several datasets, demonstrating promising results.

Sparse representation-based noise reduction for BOTDR monitoring signals in foundation pit anchor cables

Abstract Brillouin optical time-domain reflectometer (BOTDR) systems are commonly challenged by low signal-to-noise ratio (SNR) in foundation pit monitoring. This study proposes a noise-suppression method for BOTDR signals utilizing sparse representation (SR). The method involves creating an initial dictionary from the eigenvectors of the normalized graph Laplace matrix. The K-singular value decomposition and orthogonal matching pursuit algorithms are combined to update the dictionary and coefficient matrix, facilitating the SR of the signal’s intrinsic features and the removal of random noise. This results in improved quality of the reconstructed signal. An experimental system for BOTDR temperature sensing was developed to assess the algorithm’s denoising capabilities. The algorithm showed significant improvements in SNR and reductions in sample entropy (SE) compared to techniques such as wavelet threshold denoising, empirical wavelet transform, and empirical mode decomposition. Specifically, the average SNR increase was 27.4%, 15.4%, 13.1%, and 17.9%, while the average SE decrease was 24.4%, 16.0%, 15.4%, and 47.9% for the respective comparisons. The proposed Laplace-based dictionary also outperformed the discrete cosine transform dictionary. Field tests were conducted at the Beijing Stomatological Hospital, where the algorithm applied to on-site anchor cable fiber optic monitoring signals, achieving an average SE decrease of 45.2%. The research provides an effective denoising method for the application of BOTDR technology in foundation pit monitoring, underscoring the approach’s novelty and practical application.

Fault diagnosis for multiple redundancy aileron actuator based on parallel-SDP and polar sparse representation

Abstract As a critical component of aircraft flight control systems, the aileron actuator's fault directly affects the performance of flight control performance system and the overall flight safety of aircraft. Therefore, effective fault diagnosis of the aileron actuator becomes particularly important. However, with the development of redundancy design, the structure of aileron actuators more and more complex, and the fault modes are more and more diverse, which increases the difficulty of fault diagnosis significantly. To address this challenge, this study proposes a fault diagnosis method based on Parallel-SDP and Polar Sparse Representation.
First, the current residual signals of force motors are obtained using bi-step observer. Then, the residual signals are transformed into Parallel-SDP images, where each of the four petals of Parallel-SDP image generated from the corresponding channel. The Parallel-SDP image presents global fault information and capture subtle changes of residual signals, which increases the sensitivity of fault diagnosis. Subsequently, rapid single-channel fault localization is achieved by barycenter analysis of Parallel-SDP images. Finally, based on the result of fault localization, the proposed polar sparse representation algorithm is utilized for fault diagnosis of mechanical and control faults separately. Based on the dataset obtained from physical-parameter-simulation, the proposed method was validated, and the accuracy of fault diagnosis of was 99.29%, which is better than conventional fault diagnosis, meanwhile, the computational resources consumption of the proposed method is much less than deeplearning-based method, which is suitable for embedded computing system in aircraft.

Sensory and motor cortices parcellations estimated via distance-weighted sparse representation with application to autism spectrum disorder

BackgroundMotor impairments and sensory processing abnormalities are prevalent in autism spectrum disorder (ASD), closely related to the core functions of the primary motor cortex (M1) and the primary somatosensory cortex (S1). Currently, there is limited knowledge about potential therapeutic targets in the subregions of M1 and S1 in ASD patients. This study aims to map clinically significant functional subregions of M1 and S1. MethodsResting-state functional magnetic resonance imaging data (NTD = 266) from Autism Brain Imaging Data Exchange (ABIDE) were used for subregion modeling. We proposed a distance-weighted sparse representation algorithm to construct brain functional networks. Functional subregions of M1 and S1 were identified through consensus clustering at the group level. Differences in the characteristics of functional subregions were analyzed, along with their correlation with clinical scores. ResultsWe observed symmetrical and continuous subregion organization from dorsal to ventral aspects in M1 and S1, with M1 subregions conforming to the functional pattern of the motor homunculus. Significant intergroup differences and clinical correlations were found in the dorsal and ventral aspects of M1 (p < 0.05/3, Bonferroni correction) and the ventromedial BA3 of S1 (p < 0.05/5). These functional characteristics were positively correlated with autism severity. All subregions showed significant results in the ROI-to-ROI intergroup differential analysis (p < 0.05/80). LimitationsThe generalizability of the segmentation model requires further evaluation. ConclusionsThis study highlights the significance of M1 and S1 in ASD treatment and may provide new insights into brain parcellation and the identification of therapeutic targets for ASD.

Dominant duct azimuthal acoustic mode detection considering failed wall-installed microphones with amplitude or phase measurement biases

Reliable duct mode detection results are essential for aero-engine health condition monitoring and low-noise design. Harsh aero-engine measurement environments may cause biases in amplitude and phase measurements due to the failure of wall-mounted microphones, which will decrease the performance of advanced sparse representation algorithms for duct mode detection. In this paper, two strategies to detect the duct mode with the failed microphones are proposed. An optimization problem is constructed considering the low-rankness of theoretical array measurement and row-sparsity of the failed microphone measurements. The Strategy 1 is based on the recovery of the theoretical array measurement. The recovered array measurement can be further used to detect the duct mode via the sparsity-induced duct mode detection algorithm (generalized minimax-concave penalty in this paper). With the simulation, the Strategy 1 can not recover the theoretical array measurement completely. The Strategy 2 is based on the removal of the failed microphone measurements. With the simulation and experiment, it turns out that the Strategy 2 can detect the interested mode accurately.

Randomized algorithms for large-scale dictionary learning

Dictionary learning is an important sparse representation algorithm which has been widely used in machine learning and artificial intelligence. However, for massive data in the big data era, classical dictionary learning algorithms are computationally expensive and even can be infeasible. To overcome this difficulty, we propose new dictionary learning methods based on randomized algorithms. The contributions of this work are as follows. First, we find that dictionary matrix is often numerically low-rank. Based on this property, we apply randomized singular value decomposition (RSVD) to the dictionary matrix, and propose a randomized algorithm for linear dictionary learning. Compared with the classical K-SVD algorithm, an advantage is that one can update all the elements of the dictionary matrix simultaneously. Second, to the best of our knowledge, there are few theoretical results on why one can solve the involved matrix computation problems inexactly in dictionary learning. To fill-in this gap, we show the rationality of this randomized algorithm with inexact solving, from a matrix perturbation analysis point of view. Third, based on the numerically low-rank property and Nyström approximation of the kernel matrix, we propose a randomized kernel dictionary learning algorithm, and establish the distance between the exact solution and the computed solution, to show the effectiveness of the proposed randomized kernel dictionary learning algorithm. Fourth, we propose an efficient scheme for the testing stage in kernel dictionary learning. By using this strategy, there is no need to form nor store kernel matrices explicitly both in the training and the testing stages. Comprehensive numerical experiments are performed on some real-world data sets. Numerical results demonstrate the rationality of our strategies, and show that the proposed algorithms are much efficient than some state-of-the-art dictionary learning algorithms. The MATLAB codes of the proposed algorithms are publicly available from https://github.com/Jiali-yang/RALDL_RAKDL.

An initial model construction method constrained by stratigraphic sequence representation for pre‐stack seismic inversion

AbstractThe construction of an accurate and high‐resolution reservoir parameter model is crucial for reservoir characterization. However, due to the band‐limited characteristics of seismic data, the inversion results heavily rely on the accuracy of the initial model. Most existing techniques for constructing an initial model interpolate well logging data within the stratigraphic framework, neglecting the effect of the stratigraphic sequence, which compromises the reliability of the initial model. The stratigraphic sequence is essential for dividing stratigraphic evolution stages and defining a geological relationship between reservoirs within the stratigraphic framework. Therefore, an initial model construction method constrained by stratigraphic sequence representation is proposed for pre‐stack seismic inversion. The process begins with establishing the stratigraphic framework using horizon and fault data. Subsequently, the collaborative sparse representation algorithm is used to learn a joint dictionary that captures the relationship of structural features between seismic data and stratigraphic sequence from the well logging data. In the process of seismic data representation, the stratigraphic sequence is accurately represented in three‐dimensional space by sharing sparse coefficients in the joint dictionary. Finally, the elastic parameter model is constructed by integrating the stratigraphic framework, stratigraphic sequence and well logging data, providing a reliable initial model for pre‐stack seismic inversion. The main innovation of the proposed method is the three‐dimensional representation of the stratigraphic sequence. A synthetic example demonstrates that the proposed method produces a more accurate initial model than conventional interpolation methods. Additionally, when applied to field data, it yields satisfactory results even without complete S‐wave velocity well logging data.

Elliptic tangent imaging method for layered plate interfacial defects based on non-dispersive guided waves

Layered structures play an increasingly pivotal role in diverse fields such as aerospace, pipeline transportation, and petrochemical engineering. However, defects situated at the interfaces between layers pose a challenge for conventional Non-Destructive testing (NDT) methods, impeding accurate imaging. This research introduces the elliptic tangent imaging method based on interface wave modes to visualize interfacial defects within layered structures. The interface wave mode, characterized by high-frequency non-dispersive traits, facilitates precise localization of defects. Its energy concentration in the interface enhances sensitivity to interfacial defects. The elliptic tangent imaging method proposed in this paper capitalizes on the transmission coefficients of the oblique incidence technique for surface waves, enabling the concurrent determination of defect location and orientation using one pair of transducers. The application of the orthogonal matched pursuit algorithm for sparse representation of the raw signal further enhances positioning accuracy. This paper establishes an automatic detection system for interface waves, demonstrating swift transducer switching. Experimental validation of wave velocity aligns closely with theoretical calculations. In experiments focusing on interfacial defect imaging in bilayer aluminum-steel plates, the system exhibits the capability to accurately depict interfacial defects with varying orientations.

Hyperspectral Prediction Model of Nitrogen Content in Citrus Leaves Based on the CEEMDAN–SR Algorithm

Nitrogen content is one of the essential elements in citrus leaves (CL), and many studies have been conducted to determine the nutrient content in CL using hyperspectral technology. To address the key problem that the conventional spectral data-denoising algorithms directly discard high-frequency signals, resulting in missing effective signals, this study proposes a denoising preprocessing algorithm, complete ensemble empirical mode decomposition with adaptive noise joint sparse representation (CEEMDAN–SR), for CL hyperspectral data. For this purpose, 225 sets of fresh CL were collected at the Institute of Fruit Tree Research of the Guangdong Academy of Agricultural Sciences, to measure their elemental nitrogen content and the corresponding hyperspectral data. First, the spectral data were preprocessed using CEEMDAN–SR, Stein’s unbiased risk estimate and the linear expansion of thresholds (SURE–LET), sparse representation (SR), Savitzky–Golay (SG), and the first derivative (FD). Second, feature extraction was carried out using principal component analysis (PCA), uninformative variables elimination (UVE), and the competitive adaptive re-weighted sampling (CARS) algorithm. Finally, partial least squares regression (PLSR), support vector regression (SVR), random forest (RF), and Gaussian process regression (GPR) were used to construct a CL nitrogen prediction model. The results showed that most of the prediction models preprocessed using the CEEMDAN–SR algorithm had better accuracy and robustness. The prediction models based on CEEMDAN–SR preprocessing, PCA feature extraction, and GPR modeling had an R2 of 0.944, NRMSE of 0.057, and RPD of 4.219. The study showed that the CEEMDAN–SR algorithm can be effectively used to denoise CL hyperspectral data and reduce the loss of effective information. The prediction model using the CEEMDAN–SR+PCA+GPR algorithm could accurately obtain the nitrogen content of CL and provide a reference for the accurate fertilization of citrus trees.

Transient fault extraction for wind turbine generator bearing based on Bayesian biorthogonal sparse representation using adaptive redundant lifting wavelet dictionary

Aiming at the problem that it is difficult to detect effective transient impact characteristics of wind turbine generator bearing fault signals due to non-stationary and strong noise, a fault diagnosis method based on adaptive redundant lifting wavelet dictionary and Bayesian biorthogonal sparse representation (SR) algorithm is proposed. First, a Bayesian model is integrated into the biorthogonal matching pursuit (MP) algorithm to improve the use of dictionary atoms in the effective support set. Then, an adaptive redundant lifting wavelet is used to construct a dictionary matching the transient characteristics of the signal. Finally, the SR algorithm is established by integrating the Bayesian biorthogonal MP model and adaptive redundant lifting wavelet dictionary. Simulation and experimental results show that the proposed method can improve the accuracy of signal reconstruction of transient components and effectively extract bearing fault features, thus verifying the effectiveness and robustness of the method.

Information bottleneck disentanglement based sparse representation for fair classification

Unlike current state-of-the-art methods based on data augmentation and adversarial frameworks to solve the fair classification problem, this paper proposes the Information Bottleneck Disentanglement Based Sparse Representation algorithm to ensure the fairness of extracted features. The algorithm assumes that each sample is collaboratively generated by a categorical latent variable and a sensitive or category-irrelevant latent variable. To ensure that these two latent variables correctly capture their corresponding features, we impose Information Bottleneck Disentanglement constraints on them. Specifically, the Information Bottleneck is used to obtain more relevant information while compressing the amount of information. Simultaneously, a mutual information minimization constraint enhances their independence. Additionally, by employing the sparse structure, we can further disentangle the discriminative and sensitive information under supervision guidance. Therefore, the algorithm can improve the discrimination of the categorical latent variable as much as possible without extracting the sensitive data into it. Extensive experiments on five public and challenging benchmark datasets reveal the effectiveness of our proposed method, demonstrating that it can ensure fairness without sacrificing classification performance.

Face recognition technology based on low-rank joint sparse representation algorithm

With the improvement of computer computing power and the development of artificial intelligence technology, face recognition technology has made a major breakthrough, and has been popularized and applied in all areas of life. However, different face structure and pose will affect the accuracy of face recognition. To overcome the problem, a low rank joint sparse representation algorithm for face recognition is proposed. The low rank features of images are extracted by structure independent and pairwise rank decomposition methods. The extracted low rank features of the first level image and the low rank features of the second level image are sparsely represented. Finally, the residual rate model is used to classify the images, and the final result of face recognition is obtained. The experimental results show that the proposed SRP algorithm has a recognition accuracy of more than 92% in two different face recognition tests. In the mixed multi face pose test, PRS algorithm performs best in the recognition of 1, 2, 3, 4, and 5 multi face pose types, with recognition rates of 95%, 94%, 93%, 91%, and 90% respectively. The algorithm also has excellent recognition performance and robustness in identifying harsh environments such as fuzzy environments. The research content focuses on complex face recognition scenes, innovatively uses low rank to complete the extraction of face feature data, and combines sparse selection of classification features to improve the overall effect of face recognition. It has important reference value for improving the overall security and recognition rate of face recognition.

Efficient Sparse Representation for Learning With High-Dimensional Data.

Due to the capability of effectively learning intrinsic structures from high-dimensional data, techniques based on sparse representation have begun to display an impressive impact on several fields, such as image processing, computer vision, and pattern recognition. Learning sparse representations isoften computationally expensive due to the iterative computations needed to solve convex optimization problems in which the number of iterations is unknown before convergence. Moreover, most sparse representation algorithms focus only on determining the final sparse representation results and ignore the changes in the sparsity ratio (SR) during iterative computations. In this article, two algorithms are proposed to learn sparse representations based on locality-constrained linear representation learning with probabilistic simplex constraints. Specifically, the first algorithm, called approximated local linear representation (ALLR), obtains a closed-form solution from individual locality-constrained sparse representations. The second algorithm, called ALLR with symmetric constraints (ALLRSC), further obtains a symmetric sparse representation result with a limited number of computations; notably, the sparsity and convergence of sparse representations can be guaranteed based on theoretical analysis. The steady decline in the SR during iterative computations is a critical factor in practical applications. Experimental results based on public datasets demonstrate that the proposed algorithms perform better than several state-of-the-art algorithms for learning with high-dimensional data.

Kernel recursive least squares dictionary learning algorithm

An online dictionary learning algorithm for kernel sparse representation is developed in the current paper. In this framework, the input signal nonlinearly mapped into the feature space is sparsely represented based on a virtual dictionary in the same space. At any instant, the dictionary is updated in two steps. In the first step, the input signal samples are sparsely represented in the feature space, using the dictionary that has been updated based on the previous data. In the second step, the dictionary is updated. In this paper, a novel recursive dictionary update algorithm is derived, based on the recursive least squares (RLS) approach. This algorithm gradually updates the dictionary, upon receiving one or a mini-batch of training samples. An efficient implementation of the algorithm is also formulated. Experimental results over four datasets in different fields show the superior performance of the proposed algorithm in comparison with its counterparts. In particular, the classification accuracy obtained by the dictionaries trained using the proposed algorithm gradually approaches that of the dictionaries trained in batch mode. Moreover, in spite of lower computational complexity, the proposed algorithm overdoes all existing online kernel dictionary learning algorithms.

CORDIC KSVD based Online Dictionary Learning for Speech Enhancement on ASIC/FPGA Platforms

Background: The enhancement of real-world speech signals is still a challenging task to eliminate noises, namely reverberation, background, street, and babble noises. Recently learned methods like dictionary learning have become increasingly popular and showed promising results in speech enhancement. The K-means Singular Value Decomposition (KSVD) algorithm is best suited for dictionary learning among many sparse representation algorithms. Moreover, the orthogonal matching pursuit (OMP) based algorithm used for signal recovery is given. The orthogonal matching pursuit (OMP) based algorithm for signal recovery gives the best enhancement results. On the other hand, FPGAs and ASICs are widely used to accelerate speech enhancement applications. FPGAs are commonly used in healthcare and consumer applications, where speech enhancement plays a crucial role. Methods: This paper proposes a modified KSVD algorithm that can easily be implemented onto hardware platforms like FPGAs and ASICS. Instead of using the double-precision arithmetic for the singular value decomposition part of the KSVD algorithm, we proposed to use CORDIC (Coordinate Rotation Digital Computer) based QR decomposition and QR-based singular value decomposition in dictionary learning. Results: The proposed KSVD algorithm is optimal with the CORDIC algorithm that can reduce by 7-8 times the processing time. Conclusion: The finding indicates that the proposed work is best suited to FPGA or ASIC platforms.

Sparse representation scheme with enhanced medium pixel intensity for face recognition

AbstractSparse representation is an effective data classification algorithm that depends on the known training samples to categorise the test sample. It has been widely used in various image classification tasks. Sparseness in sparse representation means that only a few of instances selected from all training samples can effectively convey the essential class‐specific information of the test sample, which is very important for classification. For deformable images such as human faces, pixels at the same location of different images of the same subject usually have different intensities. Therefore, extracting features and correctly classifying such deformable objects is very hard. Moreover, the lighting, attitude and occlusion cause more difficulty. Considering the problems and challenges listed above, a novel image representation and classification algorithm is proposed. First, the authors’ algorithm generates virtual samples by a non‐linear variation method. This method can effectively extract the low‐frequency information of space‐domain features of the original image, which is very useful for representing deformable objects. The combination of the original and virtual samples is more beneficial to improve the classification performance and robustness of the algorithm. Thereby, the authors’ algorithm calculates the expression coefficients of the original and virtual samples separately using the sparse representation principle and obtains the final score by a designed efficient score fusion scheme. The weighting coefficients in the score fusion scheme are set entirely automatically. Finally, the algorithm classifies the samples based on the final scores. The experimental results show that our method performs better classification than conventional sparse representation algorithms.

An intervention study of VR sports games on the perceptual and motor abilities of children with incomplete intellectual development

Abstract Childhood is a critical stage for the development of perceptual and motor abilities, and strengthening the training of children with incomplete mental development at this stage will affect the development of motor skills during their growth. In this paper, we take VR technology as a starting point to build a perceptual model and introduce a convolutional sparse representation algorithm. First, a sparse representation with few non-zero elements is found to optimize a function consisting of a data fidelity term and a sparse induced penalty function. Then, the sum of the convolution of the filter and the convolution sparse feature map, i.e., the convolution operation, is computed to generate the translation invariants. Then the convolutional sparse coding method is introduced to the traditional unsupervised problem by calculating the minimization objective function and solving it in an iterative manner alternatively. Finally, the constituents of the signal are analyzed and the discrete equivalence of the convolution is derived based on the Fourier transform to derive the intervening variables. The experimental results showed that the mean value of the post-test of motor ability compared with the pre-test increased by 4.6 through an eight-week VR sports game training intervention study test on different children with incomplete mental development. Therefore, it is of great theoretical and practical significance to understand the characteristics of perceptual and motor abilities of children with incomplete intellectual development and to develop corresponding programs for VR sports game training according to their characteristics.

Sparse representation of acoustic emission signals and its application in pipeline leak location

The acoustic detection of pipeline leaks is strongly influenced by the associated interference and noise. In this paper, acoustic emission signals are analyzed using a sparse representation method and the main components associated with the leakage are extracted. Dictionary learning is performed using training samples composed of the leakage signals and noise signals. The measured signal is sparsely decomposed on the composite dictionary, allowing the main leakage components to be estimated. The effects of dictionary dimensionality, redundancy, sparsity constraints, and other parameters on the performance of the sparse representation algorithm are investigated. Finally, the leak location in the pipeline is determined through cross-correlation analysis of the reconstructed acoustic signals. Experimental results show that the proposed sparse representation method effectively improves the signal-to-noise ratio of the acoustic emission signals, and correspondingly improves the accuracy and reliability of pipeline leak location compared with traditional localization methods.

Incipient detection of bearing fault using impulse feature enhanced weighted sparse representation

The bearing fault impact impulses induced by the contact between components with drawback, is difficult to be detected at sprouting stage due to the interference of background noise, harmonics, random shocks, etc. In this paper, an impulse feature enhanced weighted sparse representation (IFEWSR) algorithm is proposed to accurately detect the weak bearing fault impact feature from incipient stage condition monitoring (CM) signal. Firstly, a modified fault period estimation method is presented to improve the robustness and reduce the computational complexity of recently proposed algorithms. Secondly, a novel weighting strategy on wavelet coefficients, indicated by the period-assisted corelated kurtosis of envelope spectrum (CKSES), is presented to denote the contribution of subband signals for sparse representation calculation framework. In addition, the mean normalized energy-weight deviation (MNEWD) rule is proposed to evaluate the performance of the weighting algorithm on subband signals which is blank at present. Thirdly, a novel fault feature enhancement technique is developed to better capture the bearing fault feature information. The effectiveness and superiority of the proposed method are proved by simulation and experiments. Results show that the proposed IFEWSR method provides higher accuracy for incipient fault feature extraction and outperforms other state-of-the-art methods.