Sparse Representation Coefficients Research Articles

Robust sparse representation based on fitting error decomposition

Sparse representation (SR) of a signal aims at finding the minimum number of atoms for its representation. In several practical scenarios, the signal is vulnerable to outliers and thus robustness is required for SR based algorithms. However, most existing robust schemes are designed on the assumption that the anomalies are independently distributed, which may not perform well encountering complex interferences, especially the correlated ones. To deal with this drawback, a robust SR model is proposed, where both independent and correlated outliers are considered. Specifically, the fitting error is decomposed as the combination of a low-rank component and a sparse part, corresponding to the correlated gross error and independent outlier, respectively. Then, the group sparsity of the representation coefficient is utilized. Moreover, ℓ0-norm and ℓ2,0-norm are adopted as the sparsity regularization for the sparse outlier and representation coefficients, respectively. The solutions to ℓ0/ℓ2,0-norm minimization are generated by the hard-thresholding strategy, where the decision threshold is adaptively determined using median absolute deviation operator. As for the low-rank regularization, due to the NP-hardness of rank minimization, we employ matrix logarithmic norm as the rank surrogate to lessen the approximation gap. Finally, we apply the proposed model to face recognition task, and the excellent performance demonstrates its effectiveness.

A weighted sparse classification method based on period analysis dictionary

The periodic transient shocks triggered by damages in rolling bearings are frequently overshadowed by disruptive elements such as noise and harmonics. Therefore, the extraction of fault characteristics from these disturbances to identify the health status of the bearing is crucial for fault diagnosis. This study presents a novel approach, the period analysis dictionary weighted sparse representation classification (PAD-WSRC) method, designed specifically for rolling bearings. The proposed approach incorporates Bi-damped wavelet as the dictionary wavelet atom, while accounting for the pulse characteristics induced by faults and leveraging prior knowledge of periodicity. A weighted sparse representation (SR) method was also designed, which calculates the weighted SR coefficients of samples, amplifying the local features of samples while addressing the impact of time-shift bias. In addition, the bearing fault type is identified using a mutual correlation classification criterion based on sparse approximation. Our PAD-WSRC strategy has demonstrated its effectiveness in classifying the health status of bearings across three datasets, achieving recognition accuracies of 99.75%, 99.69% and 99.17%, respectively. Comparisons with several traditional methods further underscore the effectiveness and superiority of our proposed method in classifying rolling bearing faults.

Single image super-resolution based on Bendlets analysis and structural dictionary learning

High-resolution biological tissue slice images provide opportunities for more precise observation and analysis of histopathological features. These images typically consist of enclosed contours, and Bendlets transform is an effective means to approximate such structures. In this study, we leverage Bendlet transform to incorporate multi-level image data, thereby establishing a multi-scale pyramid feature set. This approach aids in achieving a sparser representation of image textures and structures. We apply Bendlets transform to extract multi-frequency wavelet subband features and formulate structured dictionaries for both high and low resolutions based on these features. After creating these dictionaries, we compute sparse representation coefficients using the low-resolution dictionary and subsequently integrate them with the high-resolution dictionary to generate high-resolution subbands. Ultimately, through the process of inverse wavelet transformation, we completed the reconstruction of high-resolution images. This method not only significantly enhances the restoration of image details and clarity but also effectively preserves the overall structural characteristics of the original images.

Voice Vista

Blind image restoration involves leveraging prior information within an image to restore the sharpness of edges. De-blurring, on the other hand, aims to eliminate blurring artifacts caused by factors like defocus aberration or motion blur, which manifests as apparent streaking in still images of rapidly moving objects. Gaussian blur results from applying a Gaussian function to blur an image. Recent advancements in single-image methods owe their success in part to the utilization of various sparse priors for either latent images or motion blur kernels. KSR introduces an efficient kernel matrix approximation to accelerate blurring processes and achieve notable de-blur performance on digital datasets. License plate recognition serves as a critical tool for identifying over-speed vehicles or those involved in hit-and-run incidents. However, surveillance camera snapshots of speeding vehicles often suffer from motion blur, rendering them unrecognizable to the human eye and presenting a challenge to existing blind deblurring techniques. To address this, we propose a novel sparse representation-based scheme for identifying motion blur kernels. By analyzing sparse representation coefficients of the recovered image, we determine the kernel angle, and estimate the length of the motion kernel using Radon transform in Fourier domain. Our approach effectively handles large motion blur, even when license plates are unidentifiable by humans. Experimental evaluations on real-world images demonstrate the superiority of our method over several state-of-the-art blind image de-blurring algorithms.

Estimation of LFM signal parameters using RD compressed sampling and the DFRFT dictionary

In this paper, a method combining random demodulator (RD) and discrete fractional Fourier transform (DFRFT) dictionary is suggested to directly estimate the parameters of linear frequency modulation (LFM) signals from compressed sampling data. First, the RD system parameters are modified in accordance with the characteristics of the LFM signal to produce effective compressed sampling data. Next, a DFRFT dictionary is built using the fractional Fourier transform theory, and sparse representation coefficients are obtained by reconstructing the compressed sampling data using the recovery algorithm and DFRFT dictionary. The signal exhibits characteristics that make it pulse under the best fractional transform order, so the problem of signal parameter estimation can be reduced to searching for the location of the maximum value of sparse representation coefficients. The location is determined by a parameter optimization algorithm, and from there, the initial frequency and Chirp rate of the LFM signal can be estimated. Lastly, simulation and real data tests are performed to confirm that the suggested method can directly be utilized to estimate the parameter of LFM signals using compressed sampling data in addition to having high sparse representation ability for LFM signals.

An Image Denoising Model via the Reconciliation of the Sparsity and Low-Rankness of the Dictionary Domain Coefficients

Sparse coding has achieved great success in various image restoration tasks. However, if the sparse representation coefficients of the structure (low-frequency information) and texture (high-frequency information) components of the image are under the same penalty constraint, the restoration effect may not be ideal. In this paper, an image denoising model combining mixed norm and weighted nuclear norm as regularization terms is proposed. The proposed model simultaneously exploits the group sparsity of the high frequency and low-rankness of the low frequency in dictionary-domain. The mixed norm is used to constrain the high frequency part and the weighted nuclear norm is used to constrain the low frequency part. In order to make the proposed model easy to solve under the framework of alternative direction multiplier method (ADMM), iterative shrinkage threshold method and weighted nuclear norm minimization method are used to solve the two sub-problems. The validity of the model is verified experimentally through comparison with some state-of-the-art methods.

A Method Based on Random Demodulator and Waveform Matching Dictionary to Estimate LFM Signal Parameter

The compressed sampling theory provides a good idea for sampling broadband linear frequency‐modulated (LFM) signal, but the signal reconstruction after sampling should be considered when using the compressed sampling system to sample the signal. For the problem of estimating the parameters of the LFM signal under the condition of nonreconstruction, a method combining random demodulation (RD) and waveform matching (WM) dictionary is proposed in this paper. Firstly, the RD system is used to collect the compressed sampling data of LFM signal. In order to ensure the validity of the compressed sampling data, the value of the compressed sampling rate R in the RD system is discussed. Then, the feasibility of using compressed sampling data to estimate LFM signal parameters is theoretically demonstrated. According to the construction principle of waveform matching dictionary, the corresponding relationship between sparse representation coefficients, dictionary atoms, and signal parameters can be determined. Using this theory, the LFM signal parameters can be estimated. Finally, simulation and real signal experiments verify that the proposed method can realize the estimation of initial frequency and chirp rate of LFM signal when some prior information is known.

Laplacian Regularized Sparse Representation Based Classifier for Identifying DNA N4-Methylcytosine Sites via L2,1/2-Matrix Norm.

N4-methylcytosine (4mC) is one of important epigenetic modifications in DNA sequences. Detecting 4mC sites is time-consuming. The computational method based on machine learning has provided effective help for identifying 4mC. To further improve the performance of prediction, we propose a Laplacian Regularized Sparse Representation based Classifier with L2,1/2-matrix norm (LapRSRC). We also utilize kernel trick to derive the kernel LapRSRC for nonlinear modeling. Matrix factorization technology is employed to solve the sparse representation coefficients of all test samples in the training set. And an efficient iterative algorithm is proposed to solve the objective function. We implement our model on six benchmark datasets of 4mC and eight UCI datasets to evaluate performance. The results show that the performance of our method is better or comparable.

Single image super‐resolution based on sparse representation using edge‐preserving regularization and a low‐rank constraint

Sparse representation-based non-local self-similarity approaches have demonstrated promising performance in single image super-resolution reconstruction. This type of method, however, cannot always effectively preserve the key details of an image, resulting in edge artifacts and local structure blurring. To better preserve the image edge information, in this paper, a sparse representation super-resolution method based on non-local self-similarity is proposed. First, we impose slide window gradient domain guided filtering on both the low-resolution input image and the degraded restored image. Then, we utilize their difference as an edge-preserving regularization term and incorporate this regularization term into the non-local self-similarity-based sparse representation model to build a sparse coding model, which can enhance the restored high-resolution image patches’ detail information. Finally, the iterative threshold algorithm is used to calculate the sparse representation coefficients so that a high-resolution image can be estimated. Furthermore, to explore the potential structures of the subspaces spanned by similar patches, we enforce a low-rank matrix recovery technique on the generated super-resolution image, which can further refine the reconstruction quality. Experimental results prove that the new approach preserves the critical edge structures while suppressing noise and exceeding some popular methods both quantitatively and qualitatively.

Effectively Clustering Single Cell RNA Sequencing Data by Sparse Representation.

Clustering analysis has been widely used in analyzing single-cell RNA-sequencing (scRNA-seq) data to study various biological problems at cellular level. Although a number of scRNA-seq data clustering methods have been developed, most of them evaluate the similarity of pairwise cells while ignoring the global relationships among cells, which sometimes cannot effectively capture the latent structure of cells. In this paper, we propose a new clustering method SPARC for scRNA-seq data. The most important feature of SPARC is a novel similarity metric that uses the sparse representation coefficients of each cell in terms of the other cells to measure the relationships among cells. In addition, we develop an outlier detection method to help parameter selection in SPARC. We compare SPARC with nine existing scRNA-seq data clustering methods on twelve real datasets. Experimental results show that SPARC achieves the state of the art performance. By further analyzing the cell similarity data derived from sparse representations, we find that SPARC is much more effective in mining high quality clusters of scRNA-seq data than two traditional similarity metrics. In conclusion, this study provides a new way to effectively cluster scRNA-seq data and achieves more accurate clustering results than the state of art methods.

AN INFRARED AND VISIBLE IMAGE FUSION METHOD BASED ON FUZZY PULSE COUPLED NEURAL NETWORK AND SALIENCE DETECTION

Existing image fusion methods based on pulse coupled neural network (PCNN) ignore the fact that the human brain is essential to the organic combination of neural network and fuzzy system. As a result, some pixels that carry detailed information cannot activate neurons, thereby resulting in loss of details of source images and lowering the quality of fused images. To solve this problem, the present study proposed an infrared and visible image fusion method based on fuzzy pulse coupled neural network (FPCNN) and salience detection. This proposed method constructed FPCNN by combining the fuzzy theory and pulse coupled neural network. The cartoon parts obtained from the decomposition of source images by the total variation model were fused based on FPCNN. Then, salience detection of coefficients of the convolution sparse representation of the texture parts was conducted. The texture parts were fused on the basis of salience detection results. Finally, the fused cartoon and texture parts were added to obtain the fused image. The effectiveness and superiority of the proposed method were verified by experiments. Results demonstrate that compared with the most advanced seven algorithms, the proposed algorithm is superior in terms of objective evaluation indexes such as information entropy, average gradient, structural similarity, and fusion performance based on gradient. Moreover, the proposed method has good visual effect. This study provides a reference for producing high-quality all-weather images in whole-scene description. Keywords: Image fusion, Pulse coupled neural network, Salience detection, Convolution sparse representation

Hyperspectral Image Classification via Deep Structure Dictionary Learning

The construction of diverse dictionaries for sparse representation of hyperspectral image (HSI) classification has been a hot topic over the past few years. However, compared with convolutional neural network (CNN) models, dictionary-based models cannot extract deeper spectral information, which will reduce their performance for HSI classification. Moreover, dictionary-based methods have low discriminative capability, which leads to less accurate classification. To solve the above problems, we propose a deep learning-based structure dictionary for HSI classification in this paper. The core ideas are threefold, as follows: (1) To extract the abundant spectral information, we incorporate deep residual neural networks in dictionary learning and represent input signals in the deep feature domain. (2) To enhance the discriminative ability of the proposed model, we optimize the structure of the dictionary and design sharing constraint in terms of sub-dictionaries. Thus, the general and specific feature of HSI samples can be learned separately. (3) To further enhance classification performance, we design two kinds of loss functions, including coding loss and discriminating loss. The coding loss is used to realize the group sparsity of code coefficients, in which within-class spectral samples can be represented intensively and effectively. The Fisher discriminating loss is used to enforce the sparse representation coefficients with large between-class scatter. Extensive tests performed on hyperspectral dataset with bright prospects prove the developed method to be effective and outperform other existing methods.

DSRD: deep sparse representation with learnable dictionary for remotely sensed image denoising

ABSTRACT Patch-based modelling methods (i.e. sparse coding) had proven their great ability in solving the degradation problem caused by additive white Gaussian noise (AWGN) in remotely sensing images. However, these methods usually pursue surprising performance with sacrificing computational efficiency, and the learned dictionary is universal, resulting in a weak model representation flexibility. To address these issues, this paper proposes a deep sparse representation with learnable dictionary (DSRD) scheme, where the major difference from the previous sparse coding methods is that sparse representation coefficients and dictionaries are both deeply learned, acted as two modular parts to be plugged into the unfolded sparse coding model, to speed up for a stable solution as well as yielding competitive performance. The ablation studies illustrate that our DSRD strategy is efficient for a fixed solution while a flexible and powerful capacity in producing pleasing denoising performance. Meanwhile, the comparisons of quantitatively and qualitatively experimental results further demonstrate that it is effective and can generate enjoyable denoising performance that even outperforms that produced by other state-of-the-arts.

Double-Norm Constrained Image Denoising Algorithm Based on Dictionary Learning Sparsity and FCM Structure Clustering

To solve the problem of image smoothness and fuzzy edge texture information after image denoising, proposed a new image denoising method based on dictionary learning. Firstly, the external cycling principal component analysis reduces the dimensions of image data while retaining the main data and constructing the learning dictionary. Secondly, used the fuzzy c-means structure clustering method internally to implement structural constraints on learning dictionary training, which considered the internal structure of image pixels. Then, the learning dictionary under the double constraints of sparse and structural clustering is obtained by internal and external iteration. Finally, the sparse representation coefficient and redundancy dictionary are obtained by the orthogonal matching pursuit method and alternate direction multiplier method, and the denoised images are estimated and updated according to sparse coding theory. Using the grayscale image from Set12 data set, color image from the CBSD68 data set, real noise from RENOIR data set, and texture image from USC-SIPI data set. The experimental results show that compared with the model-based algorithms (KSVD, ISKR, EPLL, NCSR, and LR-GSC) and the learning-based algorithms(DnCNN, IRCNN, and FFDNet), the proposed algorithm preserves the edge and texture information of the image better, and achieves better subjective visual effects and objective numerical results, especially for the image with complex structure and content, and the running time is much less than learning-based algorithms.

Hyperspectral Detection and Unmixing of Subpixel Target Using Iterative Constrained Sparse Representation

With great significance in military and civilian applications, subpixel target detection is of great interest in hyperspectral remote sensing. The subpixel targets usually also need to be unmixed to identify their components. Traditionally, these subpixel targets are first detected and then unmixed to obtain their corresponding abundances. Therefore, target detection and target unmixing are independently performed. However, there are potential relations between these two processes that need to be investigated. In this article, we integrate these two processes using iterative constrained sparse representation. The main idea of this algorithm is that each pixel can be linearly and sparsely represented by the prior target spectra and several background endmembers extracted from its neighborhood. Moreover, the sum-to-one and nonnegativity constraints are introduced to ensure the sparse representation coefficients to have physical meaning. Specifically, the background endmembers are automatically extracted from the local background based on an iterative process. Then, the test pixel is represented by these extracted endmembers. Finally, the detection output is determined by the total target abundance and the residuals. The main innovation of this method is that it implements detection and unmixing of subpixel target simultaneously, even if the local background is contaminated by target signals. Experiments conducted on both synthetic and real hyperspectral datasets demonstrate that the proposed detector achieves an outstanding performance on detection and unmixing.

Ultrasound Image Texture Feature Learning-Based Breast Cancer Benign and Malignant Classification.

The use of ultrasound images to acquire breast cancer diagnosis information without invasion can reduce the physical and psychological pain of breast cancer patients and is of great significance for the diagnosis and treatment of breast cancer. There are some differences in the texture of breast cancer between benign and malignant cases. Therefore, this paper proposes an adaptive learning method based on ultrasonic image texture features to identify breast cancer. Specifically, firstly, we used dictionary learning and sparse representation to learn the ultrasonic image texture dictionary of benign and malignant cases, respectively, and then used the combination of the two dictionaries to represent the test image to obtain the texture distribution characteristics of the test image under the two dictionary representations, which called the sparse representation coefficient. Finally, these above features were filtered by sparse representation and sent to sparse representation classifier to establish benign and malignant classification model. 128 cases were randomly divided into training and testing sets according to 2: 1 for training and testing. The proposed method has achieved state-of-the-art results, with an accuracy of 0.9070 and the area under the receiver operating characteristic curve of 0.9459. The results demonstrate that the proposed method has the potential to be used in the clinical diagnosis of benign and malignant breast cancer.

Dimension reduction graph‐based sparse subspace clustering for intelligent fault identification of rolling element bearings

AbstractSparse subspace clustering (SSC) is a spectral clustering methodology. Since high‐dimensional data are often dispersed over the union of many low‐dimensional subspaces, their representation in a suitable dictionary is sparse. Therefore, SSC is an effective technology for diagnosing mechanical system faults. Its main purpose is to create a representation model that can reveal the real subspace structure of high‐dimensional data, construct a similarity matrix by using the sparse representation coefficients of high‐dimensional data, and then cluster the obtained representation coefficients and similarity matrix in subspace. However, the design of SSC algorithm is based on global expression in which each data point is represented by all possible cluster data points. This leads to nonzero terms in nondiagonal blocks of similar matrices, which reduces the recognition performance of matrices. To improve the clustering ability of SSC for rolling bearing and the robustness of the algorithm in the presence of a large number of background noise, a simultaneous dimensionality reduction subspace clustering technology is provided in this work. Through the feature extraction of envelope signal, the dimension of the feature matrix is reduced by singular value decomposition, and the Euclidean distance between samples is replaced by correlation distance. A dimension reduction graph‐based SSC technology is established. Simulation and bearing data of Western Reserve University show that the proposed algorithm can improve the accuracy and compactness of clustering.

Local symmetric directional pattern: A novel descriptor for extracting compact and distinctive features in face recognition

This paper presents a novel approach in feature extraction, Local Symmetric Directional Pattern (LSDP), for face recognition. The LSDP encodes the structure of facial textures based on gradient information in a simple and compact coding approach to produce more distinctive code in less time and memory than existing methods. We extract gradient information by convolving the face image with four symmetric compass masks to encode this information using directional numbers, which are related to directional information, and magnitudes of the two prominent edge responses. We also use a hybrid feature vector as a face descriptor obtained by reducing the dimensions of the LSDP feature map and classify them using the sparse representation-based classification (SRC) algorithm. Due to the high discrimination power of the extracted features, the construction of a dictionary based on the hybrid features leads to more sparse representation coefficients. As a result, it improves SRC performance in terms of recognition rate and computational speed. We perform extensive experiments to evaluate and compare the performance of our descriptor with other handcrafted descriptors and the deep learning feature under two different evaluation protocols (different dimensions of feature space and the different number of training samples) on different face databases, which have different variations of illumination, expression, and pose. Experimental results illustrate that our method achieves the highest recognition rate compared to other methods in both evaluation protocols. Especially under challenging conditions where the dimensions of the feature space or the number of training samples are low, LSDP demonstrates excellent performance.

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.

An Unsupervised Multi-Shot Person Re-Identification Method via Mutual Normalized Sparse Representation and Stepwise Learning

Due to abundant prior information and widespread applications, multi-shot based person re-identification has drawn increasing attention in recent years. In this paper, the high labeling cost and huge unlabeled data motivate us to focus on the unsupervised scenario and a unified coarse-to-fine framework is proposed, named by Mutual Normalized Sparse Representation (MNSR). Our method is an iteration procedure and each iteration involves two key steps: label estimation and metric model learning. In the former, we present a MNSR model to infer the pairwise labels of cross-camera by endowing sparse representation coefficient with the probability property. MNSR explicitly takes the mutually correlation between cameras into consideration and thus produces more accurate results. Meanwhile, we propose a probability-guided positive pairwise label prediction method to mine hard positive samples. For the latter, we learn a metric model with the estimated pairwise labels as supervision. In this procedure, we select some reliable labels for training by configuring with a stepwise learning method, rather than use all the estimated pair samples. This procedure helps to prevent the noise samples damaging the learning of discriminative metric model, especially for the initial iterations. Extensive experiments are conducted on four publicly available datasets, including PRID 2011, iLIDS-VID, SAIVT-SoftBio and MARS, and the results demonstrate the superior performance of the MNSR method in comparison with state-of-the-art unsupervised multi-shot person re-identification methods.