Sparse Representation Coefficients Research Articles

Single image super-resolution based on compressive sensing and improved TV minimization sparse recovery

In this paper, we propose a single image Super-Resolution (SR) method based on Compressive Sensing (CS) and Improved Total Variation (TV) Minimization Sparse Recovery. In the CS framework, low-resolution (LR) image is treated as the compressed version of high-resolution (HR) image. Dictionary Training and Sparse Recovery are the two phases of the method. K-Singular Value Decomposition (K-SVD) method is used for dictionary training and the dictionary represents HR image patches in a sparse manner. Here, only the interpolated version of the LR image is used for training purpose and thereby the structural self similarity inherent in the LR image is exploited. In the sparse recovery phase the sparse representation coefficients with respect to the trained dictionary for LR image patches are derived using Improved TV Minimization method. HR image can be reconstructed by the linear combination of the dictionary and the sparse coefficients. The experimental results show that the proposed method gives better results quantitatively as well as qualitatively on both natural and remote sensing images. The reconstructed images have better visual quality since edges and other sharp details are preserved.

A Novel Gene Selection Method Based on Sparse Representation and Max-Relevance and Min-Redundancy

Gene selection method as an important data preprocessing work has been followed. The criteria Maximum relevance and minimum redundancy (MRMR) has been commonly used for gene selection, which has a satisfactory performance in evaluating the correlation between two genes. However, for viewing genes in isolation, it ignores the influence of other genes. In this study, we propose a new method based on sparse representation and MRMR algorithm (SRCMRM), using the sparse representation coefficient to represent the relevance of genes and correlation between genes and categories. The SRCMRMR algorithm contains two steps. Firstly, the genes irrelevant to the classification target are removed by using sparse representation coefficient. Secondly, sparse representation coefficient is used to calculate the correlation between genes and the most representative gene with the highest evaluation. To validate the performance of the SRCMRM, our method is compared with various algorithms. The proposed method achieves better classification accuracy for all datasets. The effectiveness and stability of our method have been proven through various experiments, which means that our method has practical significance.

Robust Visual Tracking With Multitask Joint Dictionary Learning

Dictionary learning for sparse representation has been increasingly applied to object tracking, however, the existing methods only utilize one modality of the object to learn a single dictionary. In this paper, we propose a robust tracking method based on multitask joint dictionary learning. Through extracting different features of the target, multiple linear sparse representations are obtained. Each sparse representation can be learned by a corresponding dictionary. Instead of separately learning the multiple dictionaries, we adopt a multitask learning approach to learn the multiple linear sparse representations, which provide additional useful information to the classification problem. Because different tasks may favor different sparse representation coefficients, yet the joint sparsity may enforce the robustness in coefficient estimation. During tracking, a classifier is constructed based on a joint linear representation, and the candidate with the smallest joint decision error is selected to be the tracked object. In addition, reliable tracking results and augmented training samples are accumulated into two sets to update the dictionaries for classification, which helps our tracker adapt to the fast time-varying object appearance. Both qualitative and quantitative evaluations on CVPR2013 visual tracking benchmark demonstrate that our method performs favorably against state-of-the-art trackers.

Image super-resolution reconstruction based on regularization technique and guided filter

In order to improve the accuracy of sparse representation coefficients and the quality of reconstructed images, an improved image super-resolution algorithm based on sparse representation is presented. In the sparse coding stage, the autoregressive (AR) regularization and the non-local (NL) similarity regularization are introduced to improve the sparse coding objective function. A group of AR models which describe the image local structures are pre-learned from the training samples, and one or several suitable AR models can be adaptively selected for each image patch to regularize the solution space. Then, the image non-local redundancy is obtained by the NL similarity regularization to preserve edges. In the process of computing the sparse representation coefficients, the feature-sign search algorithm is utilized instead of the conventional orthogonal matching pursuit algorithm to improve the accuracy of the sparse coefficients. To restore image details further, a global error compensation model based on weighted guided filter is proposed to realize error compensation for the reconstructed images. Experimental results demonstrate that compared with Bicubic, L1SR, SISR, GR, ANR, NE+LS, NE+NNLS, NE+LLE and A+(16 atoms) methods, the proposed approach has remarkable improvement in peak signal-to-noise ratio, structural similarity and subjective visual perception.

Sparse subspace clustering for data with missing entries and high-rank matrix completion

Many methods have recently been proposed for subspace clustering, but they are often unable to handle incomplete data because of missing entries. Using matrix completion methods to recover missing entries is a common way to solve the problem. Conventional matrix completion methods require that the matrix should be of low-rank intrinsically, but most matrices are of high-rank or even full-rank in practice, especially when the number of subspaces is large. In this paper, a new method called Sparse Representation with Missing Entries and Matrix Completion is proposed to solve the problems of incomplete-data subspace clustering and high-rank matrix completion. The proposed algorithm alternately computes the matrix of sparse representation coefficients and recovers the missing entries of a data matrix. The proposed algorithm recovers missing entries through minimizing the representation coefficients, representation errors, and matrix rank. Thorough experimental study and comparative analysis based on synthetic data and natural images were conducted. The presented results demonstrate that the proposed algorithm is more effective in subspace clustering and matrix completion compared with other existing methods.

Maxdenominator Reweighted Sparse Representation for Tumor Classification

The classification of tumors is crucial for the proper treatment of cancer. Sparse representation-based classifier (SRC) exhibits good classification performance and has been successfully used to classify tumors using gene expression profile data. In this study, we propose a three-step maxdenominator reweighted sparse representation classification (MRSRC) method to classify tumors. First, we extract a set of metagenes from the training samples. These metagenes can capture the structures inherent to the data and are more effective for classification than the original gene expression data. Second, we use a reweighted regularization method to obtain the sparse representation coefficients. Reweighted regularization can enhance sparsity and obtain better sparse representation coefficients. Third, we classify the data by utilizing a maxdenominator residual error function. Maxdenominator strategy can reduce the residual error and improve the accuracy of the final classification. Extensive experiments using publicly available gene expression profile data sets show that the performance of MRSRC is comparable with or better than many existing representative methods.

The Research of Reproducibility and Non-redundancy Feature Selection Methods in Radiomics

“Radiomics” is a process of extracting a great quantity of descriptive features from biomedical images that can be used for prognosis. One of the major challenges of radiomics is to acquire the features that reproducibility and non-redundancy. The reproducibility of features dependent on the segmentation algorithm, and it should provide an accurate and reproducible result. In this study, a semi-automated segmentation method based on, which has an good effect for gray scale inhomogeneous of tumors was used to get tumor region for computed tomographic (CT) images of 35 non–small cell lung cancer (NSCLC) patients. A set of features (125 3D and 92 2D) was computed for each tumor region in the test/retest data set. In terms of comparing the intra-class correlation coefficient (ICC) with manual segmentation method in feature extracting, it is indicated that the features obtained by the method of on CV model has a better representative. A series quantitative feature of better reproducibility could be obtained. However, these features were redundant. A feature selection method based on sparse representation coefficient (SRC) was used to filter these redundant features. It is indicated that the features obtained by SRC have better non-redundancy through comparison the selection methods based on Pearson correlation coefficient (PCC) and symmetrical uncertainty (SU). Thus quantitative image features that reproducibility and non-redundancy provide informative and prognostic biomarkers for NSCLC.

Improved feature extraction using structured Fisher discrimination sparse coding scheme for machinery fault diagnosis

Vibration signals reflecting different kinds of machinery conditions are very useful for fault diagnosis. However, vibration signal characteristics are not the same for different types of equipment and patterns of failure. This available information is often lost in structureless condition diagnosis models. We propose a structured Fisher discrimination sparse coding–based fault diagnosis scheme to improve the feature extraction procedure considering both efficiency and effectiveness. There are three major components: (1) a structured dictionary for synthesizing the vibration signals that is learned by structure Fisher discrimination dictionary learning, (2) a tree-structured sparse coding to extract sparse representation coefficients from vibration signals to represent fault features, and (3) a support vector machine’s classifier on the features to recognize different faults. The proposed algorithm is verified on a standard bearing fault data set and a worm gear fault experiment. Test results have proved that the proposed method can achieve better performance with considerable efficiency and generalization ability.

Digital Watermarking Processing Technique Based on Overcomplete Dictionary

A novel sparse domain-based information hiding framework is proposed in this paper to attach the watermarking signal to the most significant sparse components of the host signal over the pre-defined overcomplete dictionary. The adaptive sparse domain can be utilized to embed watermarking logo with better security and robustness. This can be realized owing to the fact that, not only the sparse domain can be customized from the given samples, but also the sparse transform coefficients of the original watermarking signal can be embedded, which provides inherent privacy. This paper provides two kinds of methods that embed watermark directly and embed the sparse representation coefficients of watermarking logo, and analyzes the condition of uniqueness of the sparse solution. Experimental results demonstrate the superiority of the proposed sparse domain digital watermarking technique over the traditional frequency domain or spatial domain schemes.

An AK-BRP dictionary learning algorithm for video frame sparse representation in compressed sensing

Sparsifying transform is an important prerequisite in compressed sensing. And it is practically significant to research the fast and efficient signal sparse representation methods. In this paper, we propose an adaptive K-BRP (AK-BRP) dictionary learning algorithm. The bilateral random projection (BRP), a method of low rank approximation, is used to update the dictionary atoms. Furthermore, in the sparse coding stage, an adaptive sparsity constraint is utilized to obtain sparse representation coefficient and helps to improve the efficiency of the dictionary update stage further. Finally, for video frame sparse representation, our adaptive dictionary learning algorithm achieves better performance than K-SVD dictionary learning algorithm in terms of computation cost. And our method produces smaller reconstruction error as well.

Single image super-resolution by directionally structured coupled dictionary learning

In this paper, a new algorithm is proposed based on coupled dictionary learning with mapping function for the problem of single-image super-resolution. Dictionaries are designed for a set of clustered data. Data is classified into directional clusters by correlation criterion. The training data is structured into nine clusters based on correlation between the data patches and already developed directional templates. The invariance of the sparse representations is assumed for the task of super-resolution. For each cluster, a pair of high-resolution and low-resolution dictionaries are designed along with their mapping functions. This coupled dictionary learning with a mapping function helps in strengthening the invariance of sparse representation coefficients for different resolution levels. During the reconstruction phase, for a given low-resolution patch a set of directional clustered dictionaries are used, and the cluster is selected which gives the least sparse representation error. Then, a pair of dictionaries with mapping functions of that cluster are used for the high-resolution patch approximation. The proposed algorithm is compared with earlier work including the currently top-ranked super-resolution algorithm. By the proposed mechanism, the recovery of directional fine features becomes prominent.

A Soft Decision Rule for Sparse Signal Modeling via Dempster–Shafer Evidential Reasoning

Recently, the problem of recovering sparse linear representation of a query in terms of a redundant dictionary has received great interest. The query sample is represented as a linear combination of the atoms of the dictionary. The unique representation is obtained via sparsity constraint, and the decision is made in terms of the characteristics of representation on reconstruction. The decision rule for sparse signal modeling can be viewed as a typical application of Bayesian estimation, where the likelihood function is inversely proportional to the reconstruction error. Different from the conventional rule, where the decision is directly made according to the overall reconstruction error associated with each class, this letter proposes a soft decision via Dempster–Shafer theory of evidence. To model the imprecision on uncertainty measurement, we introduce the samplewise ambiguity and the classwise ambiguity during the quantification of probability mass. Each sample that participates in the recovery of the query is considered as an item of evidence that supports certain hypothesis in regard to the class membership of query. The amount of evidence is quantified by a function of the distance between the query and the weighted training sample, where the weights result from the sparse representation coefficient. Then, various pieces of evidence derived from the candidate samples are pooled by means of Dempster's rule of combination, from which a soft decision can be reached.

Robust Blur Kernel Estimation for License Plate Images From Fast Moving Vehicles

As the unique identification of a vehicle, license plate is a key clue to uncover over-speed vehicles or the ones involved in hit-and-run accidents. However, the snapshot of over-speed vehicle captured by surveillance camera is frequently blurred due to fast motion, which is even unrecognizable by human. Those observed plate images are usually in low resolution and suffer severe loss of edge information, which cast great challenge to existing blind deblurring methods. For license plate image blurring caused by fast motion, the blur kernel can be viewed as linear uniform convolution and parametrically modeled with angle and length. In this paper, we propose a novel scheme based on sparse representation to identify the blur kernel. By analyzing the sparse representation coefficients of the recovered image, we determine the angle of the kernel based on the observation that the recovered image has the most sparse representation when the kernel angle corresponds to the genuine motion angle. Then, we estimate the length of the motion kernel with Radon transform in Fourier domain. Our scheme can well handle large motion blur even when the license plate is unrecognizable by human. We evaluate our approach on real-world images and compare with several popular state-of-the-art blind image deblurring algorithms. Experimental results demonstrate the superiority of our proposed approach in terms of effectiveness and robustness.

Image Denoising Algorithm Based on Non Related Dictionary Learning

In allusion to the partial texture information loss during image deniosing process, an image denoising algorithm based on non related dictionary learning is proposed in this article. In this algorithm, the noise image is firstly divided into mutually overlapped image blocks, and a certain quantity of these image blocks are randomly selected for subsequent dictionary learning; then, non related dictionary learning technology is adopted to obtain the redundant dictionary with relatively strong irrelevance; finally, the sparse encoding algorithm is adopted to obtain the sparse representation coefficient of each image block in the redundant dictionary, and such sparse representation coefficients are used to recover the original image. The experiment result shows: since the redundant dictionary obtained through non related dictionary learning technology can strongly represent the image texture information, PSNR (Peak Signal to Noise Ratio) of the algorithm proposed in this article is superior to that of the existing advanced algorithm, and the algorithm can well keep the image detail and texture information, thus to improve visual effect.

Zero‐shot learning by exploiting class‐related and attribute‐related prior knowledge

The existing attribute-based zero-shot learning models at different levels ignore some necessary prior knowledge. It is essential to improve classification accuracy of zero-shot learning that how to mine attribute-related and class-related prior knowledge further being incorporated into the attribute prediction models. For the mining of class-related prior knowledge, measurement of the class–class correlation by using whitened cosine similarity is proposed. Likewise for the mining of attribute-related prior knowledge, measurements of the attribute–class and attribute–attribute correlation are proposed by using sparse representation coefficient. Therefore, a novel indirect attribute prediction (IAP) model is presented by exploiting class-related and attribute-related prior knowledge (IAP_CAPK). Experimental results on animals with attributes and a-Pascal/a-Yahoo datasets show that, when compared with IAP and direct attribute prediction, the proposed IAP_CAPK not only yields more accurate attribute prediction and zero-shot image classification, but also achieves much higher computational efficiency.

Sparsity embedding projections for sparse representation-based classification

Sparse representation-based classification (SRC) has become a powerful tool for image recognition. SRC sparsely encodes a test sample over all training samples and then classifies the test sample into the class that generates the minimal reconstruction residual. However, in many real-world applications, nuisances (e.g. illuminations, view directions, pixel corruptions, and occlusion, etc.) may make the representation coefficients of a test sample associated with the training samples from another class greatly larger than those associated with the training samples from the correct class. As a result, the reconstruction residual of the test sample with respect to the other class is smaller than that with respect to the correct class. This inevitably brings a wrong classification of SRC. To address this issue, we propose a sparsity embedding projections (SEP) method, which seeks a low-dimensional embedding subspace where the sparse representation coefficients of a test sample associated with the training samples from the correct class are enlarged, and simultaneously those associated with the training samples from all of the other classes are compressed. Specially, given a training data matrix, SEP tries to find a linear transformation by enhancing the intraclass reconstructive relationship meanwhile suppressing the interclass reconstructive relationship in the low-dimensional embedding subspace. Experimental results on the COIL-20, Extend Yale B, and AR databases show that the proposed method is more effective and robust than other state-of-the-art feature extraction methods with respect to SRC.

Covariance-Assisted Matching Pursuit

We consider the problem of greedy sparse approximation in the presence of noise, given a-priori knowledge of the sparse coefficients’ covariance and mean. The proposed Covariance-Assisted Matching Pursuit (CAMP) combines the a-priori knowledge by leveraging the Gauss-Markov theorem, and provides significantly better performance than the classical Orthogonal Matching Pursuit (OMP). This improvement is achieved by solving in each matching pursuit stage a weighted least-squares problem that provides the best linear unbiased estimator of the sparse representation. The covariance and mean of the sparse representation coefficients can be estimated by a simple procedure from training data, and the advantage of the proposed approach is demonstrated for the tasks of denoising and inpainting 150,000 patches from natural images.

Nearest Regularized Joint Sparse Representation for Hyperspectral Image Classification

By means of a sparse collaborative representation mechanism, sparse-representation-based classifiers show a superior performance in hyperspectral image (HSI) classification. Exploiting the similarity and distinctiveness of HSI neighboring pixels, we propose a new nearest regularized joint sparse representation (NRJSR) classification method in this letter. In the classification process of the central test pixel, the weights of different neighboring pixels and the sparse representation coefficients of different training samples are optimized simultaneously within a regularized sparsity model, which can obtain adaptive weights with good joint sparse representation ability. An alternative iteration strategy is used to solve the regularized joint sparsity model. The proposed NRJSR algorithm is tested on two benchmark HSI data sets. Experimental results demonstrate that the proposed algorithm performs better than other sparsity-based algorithms and spectral and spectral–spatial support vector machine classifiers.

Compressed Sensing, Pseudodictionary-Based, Superresolution Reconstruction

The spatial resolution of digital images is the critical factor that affects photogrammetry precision. Single-frame, superresolution, image reconstruction is a typical underdetermined, inverse problem. To solve this type of problem, a compressive, sensing, pseudodictionary-based, superresolution reconstruction method is proposed in this study. The proposed method achieves pseudodictionary learning with an available low-resolution image and uses theK-SVD algorithm, which is based on the sparse characteristics of the digital image. Then, the sparse representation coefficient of the low-resolution image is obtained by solving the norm ofl0minimization problem, and the sparse coefficient and high-resolution pseudodictionary are used to reconstruct image tiles with high resolution. Finally, single-frame-image superresolution reconstruction is achieved. The proposed method is applied to photogrammetric images, and the experimental results indicate that the proposed method effectively increase image resolution, increase image information content, and achieve superresolution reconstruction. The reconstructed results are better than those obtained from traditional interpolation methods in aspect of visual effects and quantitative indicators.

A sparse Bayesian learning based scheme for multi-movement recognition using sEMG.

This paper proposed a feature extraction scheme based on sparse representation considering the non-stationary property of surface electromyography (sEMG). Sparse Bayesian learning was introduced to extract the feature with optimal class separability to improve recognition accuracy of multi-movement patterns. The extracted feature, sparse representation coefficients (SRC), represented time-varying characteristics of sEMG effectively because of the compressibility (or weak sparsity) of the signal in some transformed domains. We investigated the effect of the proposed feature by comparing with other fourteen individual features in offline recognition. The results demonstrated the proposed feature revealed important dynamic information in the sEMG signals. The multi-feature sets formed by the SRC and other single feature yielded more superior performance on recognition accuracy, compared with the single features. The best average recognition accuracy of 94.33% was gained by using SVM classifier with the multi-feature set combining the feature SRC, Williston amplitude (WAMP), wavelength (WL) and the coefficients of the fourth order autoregressive model (ARC4) via multiple kernel learning framework. The proposed feature extraction scheme (known as SRC + WAMP + WL + ARC4) is a promising method for multi-movement recognition with high accuracy.