Sparse Coefficients Research Articles

Kernel eigenmaps based multiscale sparse model for hyperspectral image classification

Hyperspectral imaging (HSI) is the emerging method that combines traditional imaging and spectroscopy to provide the image with both the spatial and spectral information of the object present in the image. The major challenges of the existing techniques for HSI classification are the high dimensionality of data and its complexity in classification. This paper devises a new technique to classify the HSI named Spatial–Spectral Schroedinger Eigen Maps based Multi-scale adaptive sparse representation (S2SEMASR). In this, two different phases are employed for the accurate classification of the HSI, namely, Schroedinger Eigen maps (SE) based spatial–spectral feature extraction and multi-scale adaptive sparse classification for the feature extracted image. SE makes use of spatial–spectral cluster potentials which allows the extraction of features that best describes the characteristics of different classes of HSI. The multiscale adaptive sparse representation (MASR) applied over the SE features provides the sparse coefficients that includes distinct scale level sparsity with same class level sparsity. With the obtained coefficients, the class label of each pixel is determined. The proposed HSI classifier well utilizes the spectral and spatial characteristics to exploit the within-class variability and thus reduces the misclassification of similar test pixels Experimental results demonstrated that the proposed S2SEMASR approach outperforms the traditional results both qualitatively and quantitatively with an overall accuracy of 98.3%.

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.

Combination of sparsity of direct waves and detection of signal for distant speech enhancement

A joint dereverberation and denoising framework is proposed for enhancement of distant speech in a conference room. The sparsity of speech multipath propagation is exploited by a microphone array for suppressing late reverberation. The dereverberation speech is transformed to solve a minimization problem where the sparse prediction coefficients are estimated by a least-square iteration algorithm. The residual noise components are removed by iteratively reconstructing the time–frequency spectrum of speech signals. Detection of speech presence is carried out over each cell of the spectrum based on the Bayes rule. The data analysis and the real-time processing results have shown that the proposed joint framework outperforms the existing approaches in terms of objective metrics of speech quality.

A novel robust zero-watermarking algorithm for audio based on sparse representation

Behind the prevalence of multimedia technology, digital copyright disputes are becoming increasingly serious. The digital watermarking prevention technique against the copyright infringement needs to be improved urgently. Among the proposed technologies, zero-watermarking has been favored recently. In order to improve the robustness of the zero-watermarking, a novel robust audio zerowatermarking method based on sparse representation is proposed. The proposed scheme is mainly based on the K-singular value decomposition (K-SVD) algorithm to construct an optimal over complete dictionary from the background audio signal. After that, the orthogonal matching pursuit (OMP) algorithm is used to calculate the sparse coefficient of the segmented test audio and generate the corresponding sparse coefficient matrix. Then, the mean value of absolute sparse coefficients in the sparse matrix of segmented speech is calculated and selected, and then comparing the mean absolute coefficient of segmented speech with the average value of the selected coefficients to realize the embedding of zero-watermarking. Experimental results show that the proposed audio zero-watermarking algorithm based on sparse representation performs effectively in resisting various common attacks. Compared with the baseline works, the proposed method has better robustness.

Minimum variance Lamb wave imaging based on weighted sparse decomposition coefficients in quasi-isotropic composite laminates

Lamb wave is a promising means for active structural health monitoring and nondestructive evaluation of laminated composite plates. The inevitable reflections from structural geometric boundaries and other interferences limits the imaging performance of many existing imaging methods. The image generated through the well-known delay-and-sum method holds a wide mainlobe width and high level of sidelobes. Although the sparse reconstruction method is free from those deficiencies, it is sensitive to the regularization parameter. To overcome those limitations, a Lamb wave imaging method to locate anomalies or damage in laminated composite plates is proposed. The scattering signals are sparsely decomposed one by one with a prior weights penalized on the undetermined sparse coefficients, and the minimum variance distortionless response algorithm is adopted to process those sparse coefficients so as to generate the image. Experimental results on a quasi-isotropic laminated composite plate demonstrate the effectiveness of the proposed method.

Smooth non-negative sparse representation for face and handwritten recognition

In sparse representation problem, there is always interest to reduce the solution space by introducing additional constraints. This can lead to efficient application-specific algorithms. Despite known advantages of sparsity and non-negativity for image data representation, limited studies have addressed these characteristics simultaneously, due to the challenges involved. In this paper, we propose a novel inexpensive sparse non-negative reconstruction method. We utilise a non-negativity penalty term within a convex function while imposing sparsity at the same time. Our method, termed as SnSA (smooth non-negative sparse approximation) applies a novel thresholding strategy on the sparse coefficients during the minimisation of the proposed convex function. The main advantage of SnSA algorithm is that hard zeroing the negative samples which leads to unstable and non-optimal sparse solution is avoided. Instead, a differentiable smoothing function is proposed that allows gradual suppression of negative samples leading to a sparse non-negative solution. This way, the algorithm is driven towards a solution with a balance in maximising the sparsity and minimising the reconstruction error. Our numerical and experimental results on both synthetic signals and well-established face and handwritten image databases, indicate higher classification performance of the proposed method compared to the state-of-the-art techniques.

Atom specific multiple kernel dictionary based Sparse Representation Classifier for medium scale image classification

Kernel based Sparse Representation Classifier (KSRC) can classify images with acceptable performance. In addition, Multiple Kernel Learning based SRC (MKL-SRC) computes the weighted sum of multiple kernels in order to construct a unified kernel while the weight of each kernel is calculated as a fixed value in the training phase. In this paper, an MKL-SRC with non-fixed kernel weights for dictionary atoms is proposed. Kernel weights are embedded as new variables to the main KSRC goal function and the resulted optimization problem is solved to find the sparse coefficients and kernel weights simultaneously. As a result, an atom specific multiple kernel dictionary is computed in the training phase which is used by SRC to classify test images. Also, it is proved that the resulting optimization problem is convex and is solvable via common algorithms. The experimental results demonstrate the effectiveness of the proposed approach.

Multi-label feature selection via manifold regularization and dependence maximization

Feature selection is able to select more discriminative features for classification and plays an important role in multi-label learning to alleviate the effect of the curse of dimensionality. Recently, the multi-label feature selection methods based on the sparse regression model have received increasing attentions. However, most of these methods directly project original data space to label space in the regression model, which is inappropriate because the linear assumption between data space and label space doesn't hold in most cases. In the paper, we propose a feature selection method named multi-label feature selection via manifold regularization and dependence maximization (MRDM). In the regression model of MRDM, the original data space is projected to a low-dimensional manifold space, which not only has the same topological structure with the original data, but also has a strong dependence with the class labels. Then, an objective function involving l2,1-norm regularization is formulated, and an alternating optimization-based iterative algorithm is designed to obtain the sparse coefficients for multi-label feature selection. Extensive experiments on various multi-label data sets demonstrate the superiority of the proposed method compared with some state-of-the-art multi-label feature selection methods.

A novel method based on matching pursuit decomposition of gait signals for Parkinson’s disease, Amyotrophic lateral sclerosis and Huntington’s disease detection

Background and ObjectiveAn accurate detection of neurodegenerative diseases (NDDs) definitely improves the life of patients and has attracted growing attention. MethodsIn this paper, a general automatic method for detection of Parkinson’s disease (PD), Amyotrophic lateral sclerosis (ALS) and Huntington’s disease (HD) has been proposed based on the localized time–frequency information of gait signals. The new main part of the detection method is to obtain a small set of sparse coefficients for the local representation of gait signals with appropriate time and frequency resolution. For this purpose, a hybrid feature set based on sparse matching pursuit decomposition and two sets of nonlinear and linear features has been developed. Then, principal components of the proposed feature have been analyzed using a sparse coding classifier.ResultsThe proposed approach has achieved high average accuracy rates of 93%, 94%, and 97% for PD, ALS, and HD detection, respectively. ConclusionsThe obtained results have indicated that combination of time and frequency information of the gait signals through adaptive localized window length in MP makes it more efficient in comparison with the existing time, frequency or other time–frequency gait parameters. The great potential of nonlinear sparse features for PD and HD detection and linear ones for ALS detection has also been shown.

Infrared and visible image fusion based on convolutional sparse representation and guided filtering

Infrared and visible image fusion is a hot research direction in the fields of computer vision and image processing, and it is a common multimodal image fusion. An effective image fusion algorithm via convolutional sparse representation (CSR) and guided filtering is proposed for fusing infrared and visible images in this paper. First, a series of dictionary filters are trained by the CSR strategy, and the smooth image component and detailed image component are obtained by classifying those filters into high-pass filters and low-pass filters. Then two rules are designed to fuse the smooth image component and detailed image component, respectively. For the detailed image component, a weight construction method based on guided filtering is designed to get the weight maps, and the smooth image component is fused by applying the “choose-max” strategy to the corresponding sparse coefficients. Finally, the fused image is obtained by combining the fused smooth image component and detailed image component. Experimental results show that the proposed algorithm achieves good fusion results and exhibits advantages over comparison image fusion methods.

Sparse Regularization-Based Fuzzy C-Means Clustering Incorporating Morphological Grayscale Reconstruction and Wavelet Frames

The conventional fuzzy C-means (FCM) algorithm is not robust to noise and its rate of convergence is generally impacted by data distribution. Consequently, it is challenging to develop FCM-related algorithms that have good performance and require less computing time. In this article, we elaborate on a comprehensive FCM-related algorithm for image segmentation. To make FCM robust, we first utilize a morphological grayscale reconstruction (MGR) operation to filter observed images before clustering, which guarantees noise-immunity and image detail-preservation. Since real images can generally be approximated by sparse coefficients in a tight wavelet frame system, feature spaces of observed and filtered images can be obtained. Taking such features to be clustered, we investigate an improved FCM model in which a sparse regularization term is introduced into the objective function of FCM. We design a three-step iterative algorithm to solve the sparse regularization-based FCM model, which is constructed by the Lagrangian multiplier method, hard-threshold operator, and normalization operator, respectively. Such an algorithm can not only perform well for image segmentation, but also come with high computational efficiency. To further enhance the segmentation accuracy, we use MGR to filter the label set generated by clustering. Finally, a large number of supporting experiments and comparative studies with other FCM-related algorithms available in the literature are provided. The obtained results for synthetic, medical and color images indicate that the proposed algorithm has good ability for multiphase image segmentation, and performs better than other alternative FCM-related algorithms. Moreover, the proposed algorithm requires less time than most of the existing algorithms.

Face recognition via weighted non-negative sparse representation

Face recognition is one of the most important tools of identification in biometrics. Face recognition has attracted great attention in the last decades and numerous algorithms have been proposed. Different researches have shown that face recognition with Sparse Representation based Classification (SRC) has great classification performance. In some applications such as face recognition, it is appropriate to limit the search space of sparse solver because of local minima problem. In this paper, we apply this limitation via two methods. In the first, we apply the nonnegative constraint of sparse coefficients. As finding the sparse representation is a problem with very local minima, at first we use a simple classifier such as nearest subspace and then add the obtained information of this classifier to the sparse representation problem with some weights. Based on this view, we propose Weighted Non-negative Sparse Representation WNNSR for the face recognition problem. A quick and effective way to identify faces based on the sparse representation (SR) is smoothed $L_0$-norm $(SL_0)$ approach. In this paper, we solve the WNNSR problem based on the $SL_0$ idea. This approach is called Weighted Non-Negative Smoothed $L_0$ norm $(WNNSL_0)$. The simulation results on the Extended Yale B database demonstrate that the proposed method has high accuracy in face recognition better than the ultramodern sparse solvers approach.

Graph-Based Dimensionality Reduction for Hyperspectral Imagery: A Review

Hyperspectral image (HSI) contains a wealth of spectral information, which makes fine classification of ground objects possible. In the meanwhile, overly redundant information in HSI brings many challenges. Specifically, the lack of training samples and the high computational cost are the inevitable obstacles in the design of classifier. In order to solve these problems, dimensionality reduction is usually adopted. Recently, graph-based dimensionality reduction has become a hot topic. In this paper, the graph-based methods for HSI dimensionality reduction are summarized from the following aspects. 1) The traditional graph-based methods employ Euclidean distance to explore the local information of samples in spectral feature space. 2) The dimensionality-reduction methods based on sparse or collaborative representation regard the sparse or collaborative coefficients as graph weights to effectively reduce reconstruction errors and represent most important information of HSI in the dictionary. 3) Improved methods based on sparse or collaborative graph have made great progress by considering global low-rank information, local intra-class information and spatial information. In order to compare typical techniques, three real HSI datasets were used to carry out relevant experiments, and then the experimental results were analysed and discussed. Finally, the future development of this research field is prospected.

Closed-crack characterization using sparse decomposition based on nonlinear Lamb waves: a numerical study

It is known that the nonlinear interaction between closed cracks and primary elastic waves can lead to the generation of a second-harmonic component. In this work, the temporal S0-mode Lamb wave and closed-crack-interaction-induced second harmonic (abbr. closed-crack-induced second harmonic, CCISH) Lamb waves that were extracted for closed-crack characterization through a weighted and structured sparse decomposition (WSSD) algorithm. A 3D finite-element model of a thin aluminum plate based on the bilinear stiffness model is established to numerically study the nonlinear interaction between closed cracks and primary Lamb waves. Under S0-mode Lamb wave excitation, the temporal S0-mode CCISH signals are extracted from the original response using the pulse-inversion technique and a band-pass filter. A dictionary, whose columns are the normalized predicted CCISH waveforms generated by the proposed analytical CCISH generation and propagation model, is built to sparsely decompose the extracted array CCISH signals using adaptive weights. Images are generated using sparse coefficients to define the pixel values after solving the WSSD problem. Closed cracks with different locations and orientations are simulated, and imaging results show that the proposed method can characterize their location and orientation but not their length from the generated images.

Digital image watermarking in sparse domain

ABSTRACT A watermarking method based on a robust sparse domain is proposed in this paper, which integrates the secret information into the significant sparse elements of the original image. Our algorithm protects the original data by a two-way security process to embed confidential information. First of all, converting the watermark logo into a discrete transform coefficient (DCT) is the protection process. Then, using the dictionary learning method, the transformed coefficient is embedded in the selected effective sparse coefficient in the original image. The embedded logo is extracted from the selected effective sparse coefficient using the sparse orthogonal matching tracking algorithm (OMP) domain. Then, the discrete inverse transformation is performed. To check the algorithm’s efficiency, numerous specific attacks are checked. The experimental results show that the algorithm can recover the embedded watermark with precision without losing any information.

Research on Face Recognition Algorithm Based on Block CR

Partial absence of face information challenges the robustness of face recognition algorithms. In order to reduce the effect of partial information loss on face recognition, a Face Recognition Method based on partitioning Collaborative Representation (FRAPCR) is proposed in this paper. Firstly, the face image is divided into several sub-blocks. Secondly, the Collaborative Representation (CR) is used to calculate the minimum sparse representation coefficient of each sub-block and the residual between the sub-block and the corresponding samples of each class, taking the class corresponding to the minimum residual as the class to which the sub-block belongs. Thirdly, a voting mechanism is introduced to count the categories of all sub-blocks of each face image, and the category with the largest number of votes is the category to which the whole face image belongs. Through the experiments on face databases ORL, Extend Yale B, and AR by the proposed method (FRAPCR), the best partitioning way of the face image is obtained. When there is partial information missing (pixel information missing, corrosion block and occlusion) in the face image, the images in each face database is divided in its corresponding optimal partitioning way. And comparative experiments between the FRAPCR and traditional CR face recognition methods are performed. The results show that FRAPCR has high recognition rate and stable recognition effect when there is partial information missing in face images.

Hyperspectral target detection method based on spatial-spectral joint weighted dictionary learning with online updating mechanism

In recent years, many target detection methods for hyperspectral images based on sparse representation (SR) theory have been proposed and achieved good results. However, these methods still have some deficiencies. Specifically, these methods usually give the same weight to the pixels in the neighborhood when they use the spatial information, and obtain the spectral average features to replace the spectral features of the central pixel. However, the influence of each pixel in the neighborhood of the central pixel may be different. In addition, when the dictionary learning method is used for target detection, its performance depends on the constructed dictionary. To solve these problems, an innovative target detection method based on spatial-spectral joint weighted dictionary learning with an online updating mechanism is proposed. First of all, different from traditional SR method, this method integrates the spatial adaptive neighborhood information into the sparse coding stage to realize the spatial-spectral weighted joint SR. Second, the online dictionary updating mechanism and a two-step optimization method are used together to update the dictionary and sparse coding coefficients alternately, which can learn the optimal dictionary set in real time. The experimental results show that the proposed method has better performance when compared with four state-of-the-art dictionary learning-based methods for hyperspectral target detection.

Mode separation with one hydrophone in shallow water: A sparse Bayesian learning approach based on phase speed.

An approach of broadband mode separation in shallow water is proposed using phase speed extracted from one hydrophone and solved with sparse Bayesian learning (SBL). The approximate modal dispersion relation, connecting the horizontal wavenumbers (phase velocities) for multiple frequencies, is used to build the dictionary matrix for SBL. Given a multi-frequency pressure vector on one hydrophone, SBL estimates a set of sparse coefficients for a large number of atoms in the dictionary. With the estimated coefficients and corresponding atoms, the separated normal modes are retrieved. The presented method can be used for impulsive or known-form signals in a shallow-water environment while no bottom information is required. The simulation results demonstrate that the proposed approach is adapted to the environment where both the reflected and refracted modes coexist, whereas the performance of the time warping transformation degrades significantly in this scenario.

Structured sparsity assisted online convolution sparse coding and its application on weak signature detection

Due to the strong background noise and the acquisition system noise, the useful characteristics are often difficult to be detected. To solve this problem, sparse coding captures a concise representation of the high-level features in the signal using the underlying structure of the signal. Recently, an Online Convolutional Sparse Coding (OCSC) denoising algorithm has been proposed. However, it does not consider the structural characteristics of the signal, the sparsity of each iteration is not enough. Therefore, a threshold shrinkage algorithm considering neighborhood sparsity is proposed, and a training strategy from loose to tight is developed to further improve the denoising performance of the algorithm, called Variable Threshold Neighborhood Online Convolution Sparse Coding (VTNOCSC). By embedding the structural sparse threshold shrinkage operator into the process of solving the sparse coefficient and gradually approaching the optimal noise separation point in the training, the signal denoising performance of the algorithm is greatly improved. VTNOCSC is used to process the actual bearing fault signal, the noise interference is successfully reduced and the interest features are more evident. Compared with other existing methods, VTNOCSC has better denoising performance.

Adaptive Compressed Spectrum Sensing Using Neural Networks in Cognitive Radio Networks

In today's era of Internet of Things (IoT) applications, Cognitive Radio (CR) is recognized as the most promising technology to access the unused spectrum. Such CR networks can be easily built using Wide-band spectrum sensing. However, the processing of wide-band signals involves a high sampling rate. In such scenario, Compressed Spectrum Sensing (CSS) overcomes the challenges of real-time signal recovery and sampling. CSS uses Sparse signals which are widely used in many applications as they aid in processing large data. Beyond sparsity, all the real-world signals will have special structures (like Restricted Isometric property, Null space property). Moreover, it is very hard to determine the domain in which the signal is sparse. To find this we need a random measurement matrix which plays an important role in extracting the sparse coefficients of the signal. In this paper, a customized neural network is employed to identify the peculiar structures of sparse signals for efficient recovery in real time. The neural network learns and trains an adaptive measurement matrix from the sparse signals to reduce the sensing overhead. The transmitter and receiver systems are configured using Universal Software Radio Peripheral (USRP) boards with LabVIEW® and MATLAB® extensions for peer to peer communications. The implementation results depict the superior performance of neural network based recovery in assimilating the additional structures of real-time signals.