Sparse Coefficient Vector Research Articles

Sparse reconstruction of sound field using pattern-coupled Bayesian compressive sensing.

Conventional near-field acoustic holography based on compressive sensing either does not fully exploit the underlying block-sparse structures of the signal or suffers from a mismatch between the actual and predefined block structure due to the lack of prior information about block partitions, resulting in poor accuracy in sound field reconstruction. In this paper, a pattern-coupled Bayesian compressive sensing method is proposed for sparse reconstruction of sound fields. The proposed method establishes a hierarchical Gaussian-Gamma probability model with a pattern-coupled prior based on the equivalent source method, transforming the sound field reconstruction problem into recovering the sparse coefficient vector of the equivalent source strengths within the compressive sensing framework. A set of hyperparameters is introduced to control the sparsity of each element in the sparse coefficient vector of the equivalent source strengths, where the sparsity of each element is determined by both its own hyperparameters and those of its immediate neighbors. This approach enables the promotion of block sparse solutions and achieves better performance in solving for the sparse coefficient vector of the equivalent source strengths without prior information of block partitions. The effectiveness and superiority of the proposed method in reconstructing sound fields are verified by simulations and experiments.

Compressed sensing with log-sum heuristic recover for seismic denoising

The compressed sensing (CS) method, commonly utilized for restructuring sparse signals, has been extensively used to attenuate the random noise in seismic data. An important basis of CS-based methods is the sparsity of sparse coefficients. In this method, the sparse coefficient vector is acquired by minimizing the l1 norm as a substitute for the l0 norm. Many efforts have been made to minimize the lp norm (0 < p < 1) to obtain a more desirable sparse coefficient representation. Despite the improved performance that is achieved by minimizing the lp norm with 0 < p < 1, the related sparse coefficient vector is still suboptimal since the parameter p is greater than 0 rather than infinitely approaching 0 p→0+. Therefore, the CS method with the limit p→0+ is proposed to enhance the sparse performance and thus generate better denoised results in this paper. Our proposed method is referred to as the CS-LHR method because the solving process for minimizing p→0+ is the log-sum heuristic recovery (LHR). Furthermore, to improve the computational efficiency, we incorporate the majorization-minimization (MM) algorithm in this CS-LHR method. Experimental results of synthetic and real seismic records demonstrate the remarkable performance of CS-LHR in random noise suppression.

Electrocardiogram-Based Biometric Identification Using Mixed Feature Extraction and Sparse Representation.

(1) Background: The ability to recognize identities is an essential component of security. Electrocardiogram (ECG) signals have gained popularity for identity recognition because of their universal, unique, stable, and measurable characteristics. To ensure accurate identification of ECG signals, this paper proposes an approach which involves mixed feature sampling, sparse representation, and recognition. (2) Methods: This paper introduces a new method of identifying individuals through their ECG signals. This technique combines the extraction of fixed ECG features and specific frequency features to improve accuracy in ECG identity recognition. This approach uses the wavelet transform to extract frequency bands which contain personal information features from the ECG signals. These bands are reconstructed, and the single R-peak localization determines the ECG window. The signals are segmented and standardized based on the located windows. A sparse dictionary is created using the standardized ECG signals, and the KSVD (K-Orthogonal Matching Pursuit) algorithm is employed to project ECG target signals into a sparse vector-matrix representation. To extract the final representation of the target signals for identification, the sparse coefficient vectors in the signals are maximally pooled. For recognition, the co-dimensional bundle search method is used in this paper. (3) Results: This paper utilizes the publicly available European ST-T database for our study. Specifically, this paper selects ECG signals from 20, 50 and 70 subjects, each with 30 testing segments. The method proposed in this paper achieved recognition rates of 99.14%, 99.09%, and 99.05%, respectively. (4) Conclusion: The experiments indicate that the method proposed in this paper can accurately capture, represent and identify ECG signals.

An intelligent sparse feature extraction approach for music data component recognition and analysis of hybrid instruments

In this paper, a sparse feature extraction method is presented based on sparse decomposition and multiple musical instrument component dictionaries to address the challenges of existing methods in component-recognition and analysis of mixed musical instrument music data. These methods, which are often dependent on data labels, and rely primarily on frequency domain or physical features, can be improved significantly using this technique. Through the in-depth analysis of the sparse coefficient vectors, this method is capable of generating independent sparse music features that are highly interpretable and have been shown to intuitively express the composition of musical instruments, and capture the variations of emotion in the music. Consequently, this approach has great potential for application in the field of mixed musical instrument composition analysis and other time-varying signal analysis.

Moving Force Identification Based on Group Lasso and Compressed Sensing

Moving force identification (MFI) is one of the challenging tasks in bridge structural health monitoring (SHM). Especially when the vehicles get on and off the bridge, or cross bridge expansion joints and speed humps, the impact of vehicle loads on bridge structures is commonly focused and the accuracy of MFI results still needs further enhancements. To address this issue, a new MFI framework is proposed by using both group sparsity theory and compressed sensing (CS) in this study. Specifically, with the help of the relationship between moving vehicle loads and bridge responses induced by the traffic, a redundant dictionary based on CS is used to establish the motion equation of the vehicle–bridge system in conjunction with classical theory of MFI. A group structure on the sparse coefficient vector of each moving force tends to be divided into different groups (no overlapping), where sparse coefficient vectors and measurement matrices are divided in different groupings and eventually reconstructed for unknown vectors of moving forces. Additionally, the effect of different ratios of number of groups to sparsity (g/k) on the MFI results is considered. Finally, numerical simulations and experimental verifications are carried out to assess the performance and capability of the proposed framework. The illustrated results show that the group lasso could precisely reconstruct the moving forces more accurately after proper grouping. The proposed new MFI framework outperforms the traditional L2regularization or CS methods with a higher identification accuracy and a good robustness to measurement noises, which can be effectively used for the MFI problem in practice.

Virtual Kernel Discriminative Dictionary Learning With Weighted KNN for Video Analysis

Recently Kernel-Based Discriminative Dictionary (KDDL) for Video Semantic Content Analysis (VSCA) has become very popular research area, particularly in Human Computer Interactions and Computer Vision decades. Nonetheless, the existing KDDL approaches based on reconstruction error classification, coupled with sparse coefficients do not fully consider discrimination, which is essential for classification performance between video samples, despite their numerous successes. In addition, the size of video samples, an important parameter in kernel-based approaches is mostly ignored. To further improve the accuracy of video semantic classification, a VSC classification approach based on Sparse Coefficient Vector and a Virtual Kernel-based Weighted KNN is proposed in this paper. In the proposed approach, a loss function that integrates reconstruction error and discrimination is put forward. The experimental results show that this method effectively improves recognition and classification accuracy for VSCA compared with some state-of-the-art baseline approaches.

A Planar Acoustic Field Reconstruction Method Based on Fast Wave Superposition Spectrum and Sparse Sampling

Based on the fast Fourier wave superposition spectrum method, a new equivalent source method (ESM) with a sparse sampling technique is proposed. First, the equivalent source intensities are expanded on a rectangular virtual surface using a bidirectional Fourier series, resulting in a semi-analytic and half-numerical acoustic pressure expression. The Fourier coefficients result in good sparsity for continuous acoustic pressures from structural vibration sources, and the proposed sparse sampling method can further reduce correlation in the measurement matrix. Better results can be obtained by solving the l1 norm optimization problem. Finally, the method was verified using several examples. The proposed method offers two main advantages compared with the traditional compressive equivalent source method: (1) the unknown source intensity vector is expanded into a bidirectional Fourier series, thereby transforming an unknown source intensity vector into a sparse Fourier coefficient vector, which has better sparsity; (2) the proposed method constructs a random sampling matrix, which is expanded into a sparse sampling matrix by random distribution, thereby improving the reconstruction accuracy of planar near-field acoustic field compared with the traditional random position sampling method reducing correlation in the transfer matrix.

Spectral variable selection based on least absolute shrinkage and selection operator with ridge-adding homotopy

The least absolute shrinkage and selection operator (LASSO) is an established sparse representation approach for variable selection, and its performance relies on finding a good value for the regularization parameter, typically through cross-validation. However, cross-validation is a computationally intensive step and requires a properly determined search range and step size. In the present study, the ridge-adding homotopy (RAH) algorithm is applied with LASSO to overcome the aforementioned shortcomings. The homotopy algorithm can fit the entire solution of the LASSO problem by tracking the Karush-Kuhn Tucker (KKT) conditions and yields a finite number of potential regularization parameters. Considering the singularities, a M×1 random ridge vector will be added to the KKT conditions, which ensures that only one element is added to or removed from the active set. Finally, we can select the optimal regularization parameter by traversing the potential parameters with modelling and evaluation metrics. The selected variables are the nonzero elements in the sparse regression coefficient vector derived by the optimal regularization parameter. The proposed method has been demonstrated on three near-infrared (NIR) datasets with regard to wavelength selection and calibration. The results suggested that the “RAH-LASSO ​+ ​PLS” outperforms “LASSO ​+ ​PLS” and “full-wavelength PLS” in most cases. Importantly, the RAH method provides a systematic, as opposed to trial-and-error, procedure to determine the regularization parameter in LASSO.

Representation recovery via [formula omitted]-norm minimization with corrupted data

This paper studies the recovery probability of a state-of-the-art sparse recovery method, the optimization problem of YALL1, which has been rigorously used in face recognition, dense error correction, anomaly detection, etc. This work generalizes a theoretical work which is based on a special case of the optimization problem of YALL1. Furthermore, the new results cover more practical cases which do not fulfill the bouquet model proposed in the early work. The results also show that not only the special case but also some other cases of the optimization problem of YALL1; which fulfill certain conditions; can also recover any sufficiently sparse coefficient vector x when the fraction of the support of the error e is bounded away from 1 and the support of x is a very small fraction of its dimension m as m becomes large. The trade-off parameter λ in the optimization problem of YALL1 allows the recovery probability to be optimally tuned than the special case. Experimental results also show that the optimization problem of YALL1 (the Eq. (7)) with primal augmented Lagrangian optimization technique outperforms the state-of-the-art sparse recovery methods using their corresponding optimization techniques in term of the speed.

Multi-energy X-ray images fusion method based on fuzzy entropy and sparse representation for complex castings

Single-energy X-ray imaging technique cannot form all areas exposure imaging of non-uniform thickness castings at a time. Hence a multi-energy X-ray image fusion method based on fuzzy entropy and sparse representation (SR) is proposed in this paper to overcome this disadvantage. First, effective information image patches are extracted according to fuzzy entropy, thus avoiding the interference of information missing areas on the features of the castings. Then, we design a fusion strategy based on fuzzy entropy to fuse the sparse coefficient vectors. The experimental results show that the internal structure of complex castings can be completely and clearly presented using the proposed fusion method. In addition, when the proposed dictionary is applied to multi-energy X-ray images of other complex non-uniform thickness castings, the internal structure of these castings can also be presented completely and clearly.

SAR Target Recognition Using Improved Sparse Representation with Local Reconstruction

In order to handle the problem of synthetic aperture radar (SAR) target recognition, an improved sparse representation-based classification (SRC) is proposed. According to the sparse coefficient vector resulting from the global dictionary, the largest coefficient in each class is taken as the reference. Then, the surrounding neighborhoods of the sample with the largest coefficient are selected to construct the optimal local dictionary in each training class. Afterwards, the samples in the local dictionary are used to reconstruct the test sample to be identified. Finally, the decision is made according to the comparison of the reconstruction errors from different classes. In the experiments, the proposed method is verified based on the moving and stationary target acquisition and recognition (MSTAR) dataset. The results show that the proposed method has performance advantages over existing methods, which demonstrates its effectiveness and robustness.

Embedding Refinement Framework for Targeted Aspect-Based Sentiment Analysis

The state-of-the-art approaches to targeted aspect-based sentiment analysis (TABSA) are mostly built on deep neural networks with attention mechanisms. One problem is that embeddings of targets and aspects are either pre-trained from large external corpora or randomly initialized. We argue that affective commonsense knowledge and words indicative of sentiment could be used to learn better target and aspect embeddings. We therefore propose an embedding refinement framework called <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RAEC</b> ( <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</b> efining <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</b> ffective <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</b> mbedding from <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</b> ontext), in which sentiment concepts extracted from affective commonsense knowledge and word relative location information are incorporated to derive context-affective embeddings. Furthermore, a sparse coefficient vector is exploited in refining the embeddings of targets and aspects separately. In this way, embeddings of targets and aspects can capture the highly relevant affective words. Experimental results on two benchmark datasets show that our framework can be easily integrated with existing embedding-based TABSA models and achieves state-of-the-art results compared to models relying on pre-trained word embeddings or built on other embedding refinement methods.

A Discriminative Locality-Sensitive Dictionary Learning With Kernel Weighted KNN Classification for Video Semantic Concepts Analysis

Video semantic concept analysis has received a lot of research attention in the area of human computer interactions in recent times. Reconstruction error classification methods based on sparse coefficients do not consider discrimination, essential for classification performance between video samples. To further improve the accuracy of video semantic classification, a video semantic concept classification approach based on sparse coefficient vector (SCV) and a kernel-based weighted KNN (KWKNN) is proposed in this paper. In the proposed approach, a loss function that integrates reconstruction error and discrimination is put forward. The authors calculate the loss function value between the test sample and training samples from each class according to the loss function criterion, and then vote on statistical results. Finally, this paper modifies the vote results combined with the kernel weight coefficient of each class and determine the video semantic concept. The experimental results show that this method effectively improves the classification accuracy for video semantic analysis and shorten the time used in the semantic classification compared with some baseline approaches.

Multivariate empirical mode decomposition with application to SAR image target recognition

A synthetic aperture radar (SAR) target recognition method was proposed based on multivariate empirical mode decomposition (MEMD). MEMD was the general extension of traditional EMD, which could avoid the mode mixing problems. MEMD was employed to process SAR images to obtain the multi-layer intrinsic mode functions (IMF), which could better reflect the time-frequency properties of the targets. Different layers of IMFs could effectively complement each other while sharing some inner correlations because they are generated from the same target. In the classification phase, the joint sparse representation was employed to represent the IMFs. The joint sparse representation could solve several related sparse representation tasks based on the idea of multi-task learning. It could produce more precise estimations than the solutions of single tasks. According to the sparse coefficient vectors corresponding to different IMFs, the reconstruction errors of different classes for the representation of the test sample can be calculated. Afterwards, the target label of the test sample can be determined. Experiments were conducted on the Moving and Stationary Target Acquisition and Recognition (MSTAR) dataset, by comparison with existing methods under the standard operating condition, depression angle variance, noise corruption, and target occlusion, the results confirm the validity of the proposed method.

Spectral Deconfounding via Perturbed Sparse Linear Models

Standard high-dimensional regression methods assume that the underlying coefficient vector is sparse. This might not be true in some cases, in particular in presence of hidden, confounding variables. Such hidden confounding can be represented as a high-dimensional linear model where the sparse coefficient vector is perturbed. For this model, we develop and investigate a class of methods that are based on running the Lasso on preprocessed data. The preprocessing step consists of applying certain spectral transformations that change the singular values of the design matrix. We show that, under some assumptions, one can achieve the optimal $\ell_1$-error rate for estimating the underlying sparse coefficient vector. Our theory also covers the Lava estimator (Chernozhukov et al. [2017]) for a special model class. The performance of the method is illustrated on simulated data and a genomic dataset.

Robust sparse coding for one-class classification based on correntropy and logarithmic penalty function

Similar to binary and multi-class classifiers, one-class classifiers have to face the difficulty of ’curse of dimensionality’ when they are applied to deal with high-dimensional samples. As an efficient dimensionality reduction method, sparse coding tries to learn a set of over-complete bases to represent the given samples. It can effectively overcome the ’curse of dimensionality’ problem. However, the traditional sparse coding only fit for tackling Gaussian noise. When the noise within the given set of samples obey non-Gaussian distribution, the conventional sparse coding cannot obtain accurate coefficient vectors. To make sparse coding more fit for dealing with non-Gaussian noise and enhance the sparseness of the obtained coefficient vectors, correntropy is utilized to substitute its reconstruction error term and logarithmic penalty function is introduced as its regularization term. Furthermore, the obtained sparse coefficient vectors are used as the input vectors for one-class support vector machine (OCSVM). Experimental results on twenty UCI benchmark data sets and one handwritten digit data set demonstrate that the proposed method achieves better anti-noise and generalization abilities in comparison with its related approaches.

Estimation of tea quality grade using statistical identification of key variables

The uncertainty in tea classification affects the market presence of tea and damages the related economic interests. The quick and accurate identification of tea quality grades has a significant impact on the profitability of the tea market as the prices of different grades of tea quality vary greatly. In this research, 19 chemical substances that affect the quality of Huangshan Maofeng tea were detected using stoichiometry. A model-based scheme comprising the use of the stepwise regression method (SRM) was established to estimate tea quality grades. The rationale of the filtering of sparse variables in SRM is to put the elements through the preset F-statistic test to determine the selection of variables. The results of the SRM are then compared with those of elastic net and the partial least squares discriminant analysis (PLS-DA) to demonstrate the effectiveness of the proposed scheme. Furthermore, in order to verify the stability of the model, Monte Carlo experiments were conducted on the constructed models. The predictive accuracy of the SRM, PLS-DA, and elastic net algorithms were 68.75%, 75.86%, and 71.88%, respectively. The radar diagram, which is drawn according to the sparse coefficient vector obtained using SRM, illustrates that the proposed scheme can overcome the correlation between all the detection variables. It is concluded that SRM achieves the highest prediction accuracy with the least number of features, thereby simplifying the process of chemical detection, and provides a new effective scheme for batch tea-quality-grade estimation.

基于稀疏表示系数相关性的特征选择及SAR目标识别方法

基于稀疏表示系数相关性的特征选择及SAR目标识别方法

FPRSGF denoised non-subsampled shearlet transform-based image fusion using sparse representation

In this work, multiscale decomposition and sparse representation-based multimodal medical image fusion technique is proposed. An efficient denoising technique, feature-preserving regularized Savitzky–Golay filter is applied to obtain noise-free images. The filtered medical images are split into low- and high-pass subbands by non-subsampled shearlet transform (NSST). The sparse coefficient vectors of low-pass subbands are obtained from a pre-learned dictionary, and “max-L1” rule is applied to obtain the fused low-pass subband. However, high-pass subbands are fused using “max-absolute” rule. Lastly, NSST reconstruction is applied to generate the fused multimodal medical image. The non-subsampled contourlet transform, NSST-based fusion using parameter adaptive pulse coupled neural network and phase congruency techniques are also realized for comparative analysis. Multiple experiments on clean and noisy sets are performed for gray and color medical images. The fusion techniques are also tested on infrared–visible image pairs. The visual and quantitative outcomes verify that suggested technique outperforms the state-of-the-art fusion techniques.

BSBL-Based DOA and Polarization Estimation with Linear Spatially Separated Polarization Sensitive Array

The problem of multiple incident signals’ direction of arrival (DOA) and polarization estimation with linear spatially separated polarization sensitive array (SS-PSA) is investigated in sparse Bayesian learning (SBL) framework. SS-PSA is widely studied due to its low mutual coupling compared with the spatially collocated polarization sensitive array. On the one hand, the sparse representation of data model of proposed array can be expressed skillfully as a block-sparse representation. On the other hand, block sparse Bayesian learning (BSBL) algorithm has excellent performance in recovering the block-sparse signals. Therefore, in this paper, BSBL algorithm is extended to SS-PSA for DOA and polarization estimation. Firstly, a sparse representation model without parameters coupling is established, where the sparse coefficient vector is a block-sparse signal. Secondly, the expectation–maximization method in BSBL framework, i.e., BSBL-EM algorithm, is proposed to recover the block-sparse signal. Lastly, angles estimation can be obtained from the recovered sparse signal according to the intra-block correlation. Simulation results demonstrate that the BSBL-EM algorithm used in DOA and polarization estimation with SS-PSA exhibits better performance compared with Block Orthogonal Matching Pursuit algorithm and Group Basis Pursuit.