Non-negative Sparse Representation Research Articles

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.

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.

Low‐rank nonnegative sparse representation and local preservation‐based matrix regression for supervised image feature selection

Matrix regression has attracted much attention due to directly select some meaningful features from matrix data. However, most existing matrix regressions do not consider the global and local structure of the matrix data simultaneously. To this end, we propose a low-rank nonnegative sparse representation and local preserving matrix regression (LNSRLP-MR) model for image feature selection. Here, the loss function is defined by the left and right regression matrices. To capture the global structure and discriminative information of the training images and reduce the effect of heterogeneous data and noises, we impose the low-rank constraint on the self-representation error matrix and the nonnegative sparse constraint on the coefficient vector. The graph matrix can be learned adaptively through representation coefficients, so that accurate local structure information in samples can be revealed. Feature selection is performed by obtained row sparse transformation matrix. An optimization procedure and its performance are also present. Experimental results on several image datasets show that compared with the-state-of-the-art method, the average classification accuracy of the proposed method is improved by at least 1.2% and up to 3.3%. For images with noise or occlusion, the accuracy is improved significantly, up to 4%, which indicates that this method has strong robustness.

NSCR-Based DenseNet for Lung Tumor Recognition Using Chest CT Image.

Nonnegative sparse representation has become a popular methodology in medical analysis and diagnosis in recent years. In order to resolve network degradation, higher dimensionality in feature extraction, data redundancy, and other issues faced when medical images parameters are trained using convolutional neural networks. Lung tumors in chest CT image based on nonnegative, sparse, and collaborative representation classification of DenseNet (DenseNet-NSCR) are proposed by this paper: firstly, initialization parameters of pretrained DenseNet model using transfer learning; secondly, training DenseNet using CT images to extract feature vectors for the full connectivity layer; thirdly, a nonnegative, sparse, and collaborative representation (NSCR) is used to represent the feature vector and solve the coding coefficient matrix; fourthly, the residual similarity is used for classification. The experimental results show that the DenseNet-NSCR classification is better than the other models, and the various evaluation indexes such as specificity and sensitivity are also high, and the method has better robustness and generalization ability through comparison experiment using AlexNet, GoogleNet, and DenseNet-201 models.

Contribution of enhanced DWT and non-negative structured sparse representation for image super resolution: A performance analysis

The image super-resolution methods with deep learning using Convolutional Neural Network (CNN) have been producing admirable advancements. The proposed image resolution model involves the following two main analyses: (i) analysis using Adaptive Discrete Wavelet Transform (ADWT) with Deep CNN and (ii) analysis using Non-negative Structured Sparse Representation (NSSR). The technique termed as NSSR is used to recover the high-resolution (HR) images from the low-resolution (LR) images. The experimental evaluation involves two phases: Training and Testing. In the training phase, the information regarding the residual images of the dataset are trained using the optimized Deep CNN. On the other hand, the testing phase helps to generate the super resolution image using the HR wavelet subbands (HRSB) and residual images. As the main novelty, the filter coefficients of DWT are optimized by the hybrid Fire Fly-based Spotted Hyena Optimization (FF-SHO) to develop ADWT. Finally, a valuable performance evaluation on the two benchmark hyperspectral image datasets confirms the effectiveness of the proposed model over the existing algorithms.

Image classification algorithm based on stacked sparse coding deep learning model-optimized kernel function nonnegative sparse representation

Image classification has received extensive attention as an important technical means of acquiring image information. It has been widely used in various engineering fields. Although the existing traditional image classification methods have been widely applied in practical problems, there are some problems in the application process, such as unsatisfactory effects, low classification accuracy and weak adaptive ability. This is because this type of method relies on the designer’s prior knowledge and cognitive understanding of the classification task. At the same time, this method separates image feature extraction and classification into two steps for classification operation. However, the deep learning model has a powerful learning ability, which integrates the feature extraction and classification process into a whole to complete the image classification test, which can effectively improve the image classification accuracy. At the same time, the image classification method based on deep learning also has the following problems in the application process: First, it is impossible to effectively approximate the complex functions in the deep learning model. Second, the deep learning model comes with a low classifier with low accuracy. To this end, this paper introduces the idea of sparse representation into the architecture of deep learning network, comprehensively utilizes the sparse representation of good multidimensional data linear decomposition ability and the deep structural advantages of multi-layer nonlinear mapping to complete the complex function approximation in deep learning model. It constructs a deep learning model with adaptive approximation ability, which solves the function approximation problem of deep learning models. At the same time, in order to further improve the classification effect of the deep learning classifier, a sparse representation classification method based on the optimized kernel function is proposed to replace the classifier in the deep learning model, thereby improving the image classification effect. Based on the above explanation, this paper proposes an image classification algorithm based on the stacked sparse coding depth learning model-optimized kernel function nonnegative sparse representation. The experimental results show that the proposed method not only has a higher average accuracy than other mainstream methods, but also can be well adapted to various image databases. This is because the proposed method can extract more image feature information than the traditional image classification method and can better adaptively match the image information. Compared with other deep learning methods, it can better solve the problems of complex function approximation and poor classifier effect, thus further improving image classification accuracy.

Nonnegative Sparse Probabilistic Estimation for Single Sample Face Recognition

Face recognition (FR) is a hotspot in pattern recognition and image processing for its wide applications in real life. One of the most challenging problems in FR is single sample face recognition (SSFR). In this paper, we proposed a novel algorithm based on nonnegative sparse representation, collaborative presentation, and probabilistic graph estimation to address SSFR. The proposed algorithm is named as Nonnegative Sparse Probabilistic Estimation (NNSPE). To extract the variation information from the generic training set, we first select some neighbor samples from the generic training set for each sample in the gallery set and the generic training set can be partitioned into some reference subsets. To make more meaningful reconstruction, the proposed method adopts nonnegative sparse representation to reconstruct training samples, and according to the reconstruction coefficients, NNSPE computes the probabilistic label estimation for the samples of the generic training set. Then, for a given test sample, collaborative representation (CR) is used to acquire an adaptive variation subset. Finally, the NNSPE classifies the test sample with the adaptive variation subset and probabilistic label estimation. The experiments on the AR and PIE verify the effectiveness of the proposed method both in recognition rates and time cost.

Multi-focus image fusion based on non-negative sparse representation and patch-level consistency rectification

Most existing sparse representation-based (SR) fusion methods consider the local information of each image patch independently during fusion. Some spatial artifacts are easily introduced to the fused image. A sliding window technology is often employed by these methods to overcome this issue. However, this comes at the cost of high computational complexity. Alternatively, we come up with a novel multi-focus image fusion method that takes full consideration of the strong correlations among spatially adjacent image patches with NO need for a sliding window. To this end, a non-negative SR model with local consistency constraint (CNNSR) on the representation coefficients is first constructed to encode each image patch. Then a patch-level consistency rectification strategy is presented to merge the input image patches, by which the spatial artifacts in the fused images are greatly reduced. As well, a compact non-negative dictionary is constructed for the CNNSR model. Experimental results demonstrate that the proposed fusion method outperforms some state-of-the art methods. Moreover, the proposed method is computationally efficient, thereby facilitating real-world applications.

Image Classification Algorithm Based on Deep Learning-Kernel Function

Although the existing traditional image classification methods have been widely applied in practical problems, there are some problems in the application process, such as unsatisfactory effects, low classification accuracy, and weak adaptive ability. This method separates image feature extraction and classification into two steps for classification operation. The deep learning model has a powerful learning ability, which integrates the feature extraction and classification process into a whole to complete the image classification test, which can effectively improve the image classification accuracy. However, this method has the following problems in the application process: first, it is impossible to effectively approximate the complex functions in the deep learning model. Second, the deep learning model comes with a low classifier with low accuracy. So, this paper introduces the idea of sparse representation into the architecture of the deep learning network and comprehensively utilizes the sparse representation of well multidimensional data linear decomposition ability and the deep structural advantages of multilayer nonlinear mapping to complete the complex function approximation in the deep learning model. And a sparse representation classification method based on the optimized kernel function is proposed to replace the classifier in the deep learning model, thereby improving the image classification effect. Therefore, this paper proposes an image classification algorithm based on the stacked sparse coding depth learning model-optimized kernel function nonnegative sparse representation. The experimental results show that the proposed method not only has a higher average accuracy than other mainstream methods but also can be good adapted to various image databases. Compared with other deep learning methods, it can better solve the problems of complex function approximation and poor classifier effect, thus further improving image classification accuracy.

Spectral Representation vis Data-Guided Sparsity for Hyperspectral Image Super-Resolution†.

Hyperspectral imaging is capable of acquiring the rich spectral information of scenes and has great potential for understanding the characteristics of different materials in many applications ranging from remote sensing to medical imaging. However, due to hardware limitations, the existed hyper-/multi-spectral imaging devices usually cannot obtain high spatial resolution. This study aims to generate a high resolution hyperspectral image according to the available low resolution hyperspectral and high resolution RGB images. We propose a novel hyperspectral image superresolution method via non-negative sparse representation of reflectance spectra with a data guided sparsity constraint. The proposed method firstly learns the hyperspectral dictionary from the low resolution hyperspectral image and then transforms it into the RGB one with the camera response function, which is decided by the physical property of the RGB imaging camera. Given the RGB vector and the RGB dictionary, the sparse representation of each pixel in the high resolution image is calculated with the guidance of a sparsity map, which measures pixel material purity. The sparsity map is generated by analyzing the local content similarity of a focused pixel in the available high resolution RGB image and quantifying the spectral mixing degree motivated by the fact that the pixel spectrum of a pure material should have sparse representation of the spectral dictionary. Since the proposed method adaptively adjusts the sparsity in the spectral representation based on the local content of the available high resolution RGB image, it can produce more robust spectral representation for recovering the target high resolution hyperspectral image. Comprehensive experiments on two public hyperspectral datasets and three real remote sensing images validate that the proposed method achieves promising performances compared to the existing state-of-the-art methods.

Infrared and Visible Image Fusion Method by Using Hybrid Representation Learning

For remote sensing image fusion, infrared and visible images have very different brightness due to their disparate imaging mechanisms, the result of which is that nontarget regions in the infrared image often affect the fusion of details in the visible image. This letter proposes a novel infrared and visible image fusion method basing hybrid representation learning by combining dictionary-learning-based joint sparse representation (JSR) and nonnegative sparse representation (NNSR). In the proposed method, different fusion strategies are adopted, respectively, for the mean image, which represents the primary energy information, and for the deaveraged image, which contains important detail features. Since the deaveraged image contains a large amount of high-frequency details information of the source image, JSR is utilized to sparsely and accurately extract the common and innovation features of the deaveraged image, thus, accurately merging high-frequency details in the deaveraged image. Then, the mean image represents low-frequency and overview features of the source image, according to NNSR, mean image is classified well-directed to different feature regions and then fused, respectively. Such proposed method, on the one hand, can eliminate the impact on fusion result suffering from very different brightness causing by different imaging mechanism between infrared and visible image; on the other hand, it can improve the readability and accuracy of the result fusion image. Experimental result shows that, compared with the classical and state-of-the-art fusion methods, the proposed method not only can accurately integrate the infrared target but also has rich background details of the visible image, and the fusion effect is superior.

Spectral Reflectance Recovery From a Single RGB Image

The spectral reflectance is an intrinsic and discriminative characteristic of object materials and can be obtained by hyperspectral imaging. However, existing hyperspectral cameras are limited in low-spatial/temporal resolution while yet being complicated and expensive. In this paper, we present a nonnegative sparse representation based method to recover high-quality spectral reflectance from a single RGB image. Unlike previous methods, our approach learns multiple nonnegative sparse coding dictionaries from the training spectral dataset in terms of clustering results. Then, the spectral reflectance of the input RGB image is recovered based on nonnegative sparse representation, which also considers the spatial structured similarity and high correlation across spectra under the learned dictionaries. Furthermore, the illumination spectrum can be estimated with the recovered spectral reflectance under the known RGB camera spectral sensitivity. Experimental results show that the proposed method outperforms state-of-the-art spectral reflectance recovery methods in terms of both objective metrics and subjective visual quality. Besides, we show an application of our method to accurately relight scenes under the novel illumination.

Combining Non-negative Matrix Factorization and Sparse Coding for Functional Brain Overlapping Community Detection

The functional system of the human brain can be viewed as a complex network. Among various features of the brain functional network, community structure has raised significant interest in recent years. Increasing evidence has revealed that most realistic complex networks have an overlapping community structure. However, the overlapping community structure of the brain functional network has not been adequately studied. In this paper, we propose a novel method called sparse symmetric non-negative matrix factorization (ssNMF) to detect the overlapping community structure of the brain functional network. Specifically, it is formulated by combining the effective techniques of non-negative matrix factorization and sparse coding. Besides, the non-negative adaptive sparse representation is applied to construct the whole-brain functional network, based on which ssNMF is performed to detect the community structure. Both simulated and real functional magnetic resonance imaging data are used to evaluate ssNMF. The experimental results demonstrate that the proposed ssNMF method is capable of accurately and stably detecting the underlying overlapping community structure. Moreover, the physiological interpretation of the overlapping community structure detected by ssNMF is straightforward. This novel framework, we think, provides an effective tool to study overlapping community structure and facilitates the understanding of the network organization of the functional human brain.

Nonnegative Sparse Representation of Signals With a Determinant-Type Sparsity Measure Based on the DC Programming

Nonnegative sparse representation has become highly popular in certain applications in the context of signals and corresponding dictionaries that have nonnegative limitations. Applying an adaptive dictionary for sparse representation of nonnegative signals has been shown to be very effective; but constructing adaptive dictionary, i.e., dictionary learning, remains a challenge. In this paper, we attempt to design an effective and tailored algorithm for the sparse representation of nonnegative signals. We consider the so-called determinant sparsity measure formed with the determinant of the Gram matrix of sparse coefficients. Based on the determinant measure, we formulate the nonnegative dictionary learning problem that is optimization of a non-convex function. For reducing the computational complexity of the optimization, the difference of convex functions (DC) programming is employed since the non-convex function can be set to the form of difference of two convex functions. Because there are two variables in the dictionary learning problem that cannot be solved directly by DC programming, an alternation scheme is employed to treat the sparse coding and dictionary update of the dictionary learning problem alternatively with the DC programming. Our proposed novel dictionary learning algorithm has three advantages: 1) the higher recovery ratio is achieved by the proposed algorithm, even when the signals are weakly sparse; 2) the generalization ability of the proposed algorithm is greater, more often converging to a global solution than to local optimal solutions; and 3) the obtained sparse solution has a low-overlapping property that enables the solutions to be sparse and makes the proposed algorithm robust. Numerical experiments and experiments using real-world data demonstrate the effectiveness and applicability of the proposed algorithm.

Image categorization using non-negative kernel sparse representation

Sparse representation of signals have become an important tool in computer vision. In many computer vision applications such as image denoising, image super-resolution and object recognition, sparse representations have produced remarkable performances. Sparse representation models often contain two stages: sparse coding and dictionary learning. In this paper, we propose a non-linear non-negative sparse representation model: NNK-KSVD. In the sparse coding stage, a non-linear update rule is proposed to obtain the sparse matrix. In the dictionary learning stage, the proposed model extends the kernel KSVD by embedding the non-negative sparse coding. The proposed non-negative kernel sparse representation model was evaluated on several public image datasets for the task of classification. Experimental results show that by exploiting the non-linear structure in images and utilizing the ‘additive’ nature of non-negative sparse coding, promising classification performance can be obtained. Moreover, the proposed sparse representation method was also evaluated in image retrieval tasks, competitive results were obtained.

Dimensionality Reduction for Hyperspectral Data Based on Pairwise Constraint Discriminative Analysis and Nonnegative Sparse Divergence

To improve the classification accuracy of unlabeled large-scale hyperspectral data, a dimensionality reduction algorithm based on pairwise constraint discriminant analysis and nonnegative sparse divergence (PCDA-NSD) is proposed by using the feature transfer learning technology. Different from labeled sample information that is relatively difficult to acquire, pairwise constraints are a kind of useful supervision information, which can be automatically acquired without artificial interference and thus can better avoid the selection of redundant and noisy samples. Therefore, the pairwise constraint discriminant analysis method is used to learn potential discriminant information of sample sets in the source and target domains. Consequently, positively correlated constraint samples in the source and target domains share one subspace whereas positively and negatively correlated constraint samples are highly separated. Because hyperspectral data in the source and target domains often follow different distributions, a nonnegative sparse divergence is established to measure the divergence between different distributions, based on the nonnegative sparse representation method. Therefore, not only the computation load of the kernel matrix is reduced, but also the natural discriminant capacity is obtained. Experiments of a four-group hyperspectral data show that PCDA-NSD can reduce dimensionality of target data and improve classification accuracy and efficiency by adequate use of the information available in similar hyperspectral data.

Aspect-Aided Dynamic Non-Negative Sparse Representation-Based Microwave Image Classification.

Classification of target microwave images is an important application in much areas such as security, surveillance, etc. With respect to the task of microwave image classification, a recognition algorithm based on aspect-aided dynamic non-negative least square (ADNNLS) sparse representation is proposed. Firstly, an aspect sector is determined, the center of which is the estimated aspect angle of the testing sample. The training samples in the aspect sector are divided into active atoms and inactive atoms by smooth self-representative learning. Secondly, for each testing sample, the corresponding active atoms are selected dynamically, thereby establishing dynamic dictionary. Thirdly, the testing sample is represented with -regularized non-negative sparse representation under the corresponding dynamic dictionary. Finally, the class label of the testing sample is identified by use of the minimum reconstruction error. Verification of the proposed algorithm was conducted using the Moving and Stationary Target Acquisition and Recognition (MSTAR) database which was acquired by synthetic aperture radar. Experiment results validated that the proposed approach was able to capture the local aspect characteristics of microwave images effectively, thereby improving the classification performance.

Sparse representation-based image restoration via nonlocal supervised coding

Sparse representation (SR) and nonlocal technique (NLT) have shown great potential in low-level image processing. However, due to the degradation of the observed image, SR and NLT may not be accurate enough to obtain a faithful restoration results when they are used independently. To improve the performance, in this paper, a nonlocal supervised coding strategy-based NLT for image restoration is proposed. The novel method has three main contributions. First, to exploit the useful nonlocal patches, a nonnegative sparse representation is introduced, whose coefficients can be utilized as the supervised weights among patches. Second, a novel objective function is proposed, which integrated the supervised weights learning and the nonlocal sparse coding to guarantee a more promising solution. Finally, to make the minimization tractable and convergence, a numerical scheme based on iterative shrinkage thresholding is developed to solve the above underdetermined inverse problem. The extensive experiments validate the effectiveness of the proposed method.

Nonnegative matrix factorization and sparse representation for the automated detection of periodic limb movements in sleep.

Stroke is a leading cause of death and disability in adults, and incurs a significant economic burden to society. Periodic limb movements (PLMs) in sleep are repetitive movements involving the great toe, ankle, and hip. Evolving evidence suggests that PLMs may be associated with high blood pressure and stroke, but this relationship remains underexplored. Several issues limit the study of PLMs including the need to manually score them, which is time-consuming and costly. For this reason, we developed a novel automated method for nocturnal PLM detection, which was shown to be correlated with (a) the manually scored PLM index on polysomnography, and (b) white matter hyperintensities on brain imaging, which have been demonstrated to be associated with PLMs. Our proposed algorithm consists of three main stages: (1) representing the signal in the time-frequency plane using time-frequency matrices (TFM), (2) applying K-nonnegative matrix factorization technique to decompose the TFM matrix into its significant components, and (3) applying kernel sparse representation for classification (KSRC) to the decomposed signal. Our approach was applied to a dataset that consisted of 65 subjects who underwent polysomnography. An overall classification of 97% was achieved for discrimination of the aforementioned signals, demonstrating the potential of the presented method.

A non-negative sparse semi-supervised dimensionality reduction algorithm for hyperspectral data

A non-negative sparse semi-supervised dimensionality reduction algorithm is proposed for hyperspectral data by making adequate use of a few labeled samples and a large number of unlabeled samples. The objective function of the proposed algorithm consists of two terms: (1) a discriminant item is designed to analyze a few labeled samples from the global viewpoint, which can assess the separability between surface objects; (2) a regularization term is used to build a non-negative sparse representation graph based on the unlabeled samples, which can adaptively find an adjacency graph for each sample and then find valuable samples with huge information volume from the original hyperspectral data. Based on the objective function and the maximum margin criterion, a dimensionality reduction algorithm, the non-negative sparse semi-supervised maximum margin algorithm, is proposed. Experimental results on the ROSIS University and AVIRIS 92AV3C hyperspectral data sets show that the proposed algorithm can effectively utilize the unlabeled samples to achieve higher overall classification accuracy and Kappa coefficient when compared with some representative supervised, unsupervised and semi-supervised dimensionality reduction algorithms.