Joint Sparse Model Research Articles

Class-Level Joint Sparse Representation for Multifeature-Based Hyperspectral Image Classification

Recent studies show that different features can represent different characteristics of hyperspectral images, and a combination of them would have positive influence on classification. In this paper, we formulate the multifeature hyperspectral image classification as a joint sparse representation model which simultaneously represents the pixels of multiple features (spectral, shape, and texture) with a class-level sparse constraint. The proposed model enforces pixels in a small region of each type features to share the same sparsity pattern; at the same time, the pixels described by different features have freedom to adaptively choose their own appropriate atoms but still belong to the same class. Thus, the proposed model not only preserves the spatial information by joint sparse constraint but also utilizes additional complementary information from different features by class-level sparse constraint. Furthermore, we also kernelize the model to handle nonlinearity in the data. And a new version of simultaneous orthogonal matching pursuit is proposed to solve the aforementioned problems. Experiments on several real hyperspectral images indicate that the proposed algorithms provide a competitive performance when compared with several state-of-the-art algorithms.

Distributed compressed sensing based joint detection and tracking for multistatic radar system

In this paper, we present a novel distributed compressed sensing based joint detection and tracking algorithm for multistatic radar system, which significantly reduces the computational load in a centralized fusion framework. For different receivers in the multistatic radar system, their corresponding sparse vectors, which are represented in state space, share the same locations of nonzero reflection coefficients. This fits the joint sparsity model 2 (JSM-2) in distributed compressed sensing. In this paper, a novel algorithm, named distributed general similar sensing matrix pursuit (DGSSMP) algorithm, is proposed to tackle the generalized JSM-2 model when each individual sensing matrix is different and with high coherence. In contrast to the classical greedy algorithms dealing with single subspace, the proposed DGSSMP algorithm has to tackle a union of different subspaces, with each subspace corresponding to a different sensing matrix for each individual receiver. The simulation results show that in the proposed distributed compressed sensing based joint detection and tracking framework, the proposed DGSSMP algorithm together with the track before detect (TBD) scheme can effectively distinguish true targets from clutter based on the information from multiple scans.

Typical reconstruction performance for distributed compressed sensing based on ℓ2,1-norm regularized least square and Bayesian optimal reconstruction: influences of noise

A signal model called joint sparse model 2 (JSM-2) or the multiple measurement vector problem, in which all sparse signals share their support, is important for dealing with practical signal processing problems. In this paper, we investigate the typical reconstruction performance of noisy measurement JSM-2 problems for -norm regularized least square reconstruction and the Bayesian optimal reconstruction scheme in terms of mean square error. Employing the replica method, we show that these schemes, which exploit the knowledge of the sharing of the signal support, can recover the signals more precisely as the number of channels increases. In addition, we compare the reconstruction performance of two different ensembles of observation matrices: one is composed of independent and identically distributed random Gaussian entries and the other is designed so that row vectors are orthogonal to one another. As reported for the single-channel case in earlier studies, our analysis indicates that the latter ensemble offers better performance than the former ones for the noisy JSM-2 problem. The results of numerical experiments with a computationally feasible approximation algorithm we developed for this study agree with the theoretical estimation.

Robust Online Object Tracking with a Structured Sparse Representation Model

As one of the most important issues in computer vision and image processing, online object tracking plays a key role in numerous areas of research and in many real applications. In this study, we present a novel tracking method based on the proposed structured sparse representation model, in which the tracked object is assumed to be sparsely represented by a set of object and background templates. The contributions of this work are threefold. First, the structure information of all the candidate samples is utilized by a joint sparse representation model, where the representation coefficients of these candidates are promoted to share the same sparse patterns. This representation model can be effectively solved by the simultaneous orthogonal matching pursuit method. In addition, we develop a tracking algorithm based on the proposed representation model, a discriminative candidate selection scheme, and a simple model updating method. Finally, we conduct numerous experiments on several challenging video clips to evaluate the proposed tracker in comparison with various state-of-the-art tracking algorithms. Both qualitative and quantitative evaluations on a number of challenging video clips show that our tracker achieves better performance than the other state-of-the-art methods.

Exploiting Joint Sparsity for Pansharpening: The J-SparseFI Algorithm

Recently, sparse signal representation of image patches has been explored to solve the pansharpening problem. Although these proposed sparse-reconstruction-based methods lead to promising results, three issues remained unsolved: 1) high computational cost; 2) no consideration given to the possibility of mutually correlated information in different multispectral channels; and 3) requirement that the spectral responses of the panchromatic (Pan) image and the multispectral image cover the same wavelength range, which is not necessarily valid for most sensors. In this paper, we propose a sophisticated sparse image fusion algorithm, which is named “jointly sparse fusion of images” (J-SparseFI). It is based on the earlier proposed sparse fusion of images (SparseFI) algorithm and overcomes the aforementioned three drawbacks of the existing sparse image fusion algorithms. The computational problem is handled by reducing the problem size and by proposing a fully parallelizable scheme. Moreover, J-SparseFI exploits the possible signal structure correlations between multispectral channels by introducing the joint sparsity model (JSM) and sharpening the highly correlated adjacent multispectral channels together. This is done by exploiting the distributed compressive sensing theory that restricts the solution of an underdetermined system by considering an ensemble of signals being jointly sparse. J-SparseFI also offers a practical solution to overcome spectral range mismatch between the Pan and multispectral images. By means of sensor spectral response and channel mutual correlation analysis, the multispectral channels are assigned to primary groups of joint channels, secondary groups of joint channels, and individual channels. Primary groups of joint channels, individual channels, and secondary groups of joint channels are then reconstructed sequentially, by the JSM or by modified SparseFI, using a dictionary trained from the Pan image or previously reconstructed high-resolution multispectral channels. A recipe of how to choose appropriate algorithm parameters, including the most crucial regularization parameter, is provided. The algorithm is evaluated and validated using WorldView-2-like images that are simulated using very high resolution airborne HySpex hyperspectral imagery and further practically demonstrated using real WorldView-2 images. The algorithm's performance is compared with other state-of-the-art methods. Visual and quantitative analyses demonstrate the high quality of the proposed method. In particular, the analysis of the difference images suggests that J-SparseFI is superior in image resolution recovery.

Effective approach for pattern synthesis of sparse reconfigurable antenna arrays with exact pattern matching

An effective approach is presented for pattern synthesis of reconfigurable antenna arrays with non-uniformly spaced arrangements. On the basis of the joint sparse model of multiple reference patterns, the proposed approach can dynamically reconfigure multiple radiation patterns with exactly matched pattern details and minimum number of antenna elements by joint optimisation of element positions and excitations. In this study, the design of sparse reconfigurable arrays is recast as a simultaneous sparse approximation problem and solved with the multi-task Bayesian compressive sensing. The common element positions and individual element excitations for multiple radiation patterns are obtained simultaneously by searching out multiple weight vectors sharing the same prior probability. Several representative experiments are provided to validate the effectiveness of the proposed method for the design of maximally sparse reconfigurable antenna arrays with exact pattern matching.

Compressive multi-spectral imaging using self-correlations of images based on hierarchical joint sparsity models

We propose a novel multi-spectral imaging method based on compressive sensing (CS). In CS theory, the enhancement of signal sparsity is important for accurate signal reconstruction. The main novelty of the proposed method is the employment of a self-correlation of an image, that is a local intensity similarity and multi-spectral correlation, to enhance the sparsity of the multi-spectral image to be recovered. Local intensity similarity, which is based on the concept that spatial changes in intensity are likely to be similar within local regions, contributes to sparsity enhancement. Furthermore, we exploit multi-spectral correlation to improve the sparsity of the multi-spectral components to be recovered. In order to simultaneously exploit different types of characteristics (i.e., local intensity similarity and multi-spectral correlation) for representing a signal as sufficiently sparse, we introduce a hierarchical joint sparsity model in the CS image recovery process. Our experiments show that the use of a self-correlation significantly improves the performance of multi-spectral image reconstruction.

Simultaneous image fusion and demosaicing via compressive sensing

In this paper, a compressive sensing based simultaneous fusion and demosaicing method for raw data of single-chip imaging camera is introduced. In order to meet the incoherence constraints of compressive sensing theory, the popular Bayer CFA is replaced with a random panchromatic color filter array. Then, the demosaicing problem is cast as an ill-posed inverse problem inherently and the compressive sensing technology is employed to solve the inverse problem. The restored sparse coefficients of different images are further fused with ℓ1-norm of the coefficients being served as activity measurements. The final fused image is reconstructed from the fused sparse coefficients. The extended joint sparse model is further used to exploit the inter-channel correlation of different color components. The simulation results illustrated in Experimental Section demonstrate that the proposed method gives both superior quantitative and qualitative performances.

Group and Graph Joint Sparsity for Linked Data Classification

Various sparse regularizers have been applied to machine learning problems, among which structured sparsity has been proposed for a better adaption to structured data. In this paper, motivated by effectively classifying linked data (e.g. Web pages, tweets, articles with references, and biological network data) where a group structure exists over the whole dataset and links exist between specific samples, we propose a joint sparse representation model that combines group sparsity and graph sparsity, to select a small number of connected components from the graph of linked samples, meanwhile promoting the sparsity of edges that link samples from different groups in each connected component. Consequently, linked samples are selected from a few sparsely-connected groups. Both theoretical analysis and experimental results on four benchmark datasets show that the joint sparsity model outperforms traditional group sparsity model and graph sparsity model, as well as the latest group-graph sparsity model.

Joint sparsity and fidelity regularization for segmentation-driven CT image preprocessing

In this paper, we propose a novel segmentation-driven computed tomography (CT) image preprocessing approach. The proposed approach, namely, joint sparsity and fidelity regularization (JSFR) model can be regarded as a generalized total variation (TV) denoising model or a generalized sparse representation denoising model by adding an additional gradient fidelity regularizer and a stronger gradient sparsity regularizer. Thus, JSFR model consists of three terms: intensity fidelity term, gradient fidelity term, and gradient sparsity term. The interactions and counterbalance of these terms make JSFR model has the ability to reduce intensity inhomogeneities and improve edge ambiguities of a given image. Experimental results carried out on the real dental cone-beam CT data demonstrate the effectiveness and usefulness of JSFR model for CT image intensity homogenization, edge enhancement, as well as tissue segmentation.

A fast two dimensional joint linearized bregman iteration algorithm for super-resolution inverse synthetic aperture radar imaging at low signal-to-noise ratios

In practical inverse synthetic aperture radar (ISAR), the traditional imaging algorithms have low range and low cross-range resolutions while the echoes have limited bandwidth and sparse azimuth aperture in small coherent processing interval. To obtain super-resolution ISAR imaging at low signal-to-noise (SNR) ratios, this paper puts forward a novel fast two-dimensional joint linearized Bregman iteration (2D-JLBI) algorithm based on compressive sensing theory. Firstly, the radar echoes are established as a two-dimensional joint sparse representation model in the range frequency-azimuth Doppler domain. Consequently, the original two-dimensional super resolution imaging problem is converted into a two-dimensional jointly compressive reconstruction problem. Secondly, to avoid the reconstruction complexity from the vectorization of the echoes, the two-dimensional joint linearized Bregman iterative algorithm is proposed. Meanwhile, three strategies, namely the weighted residual iteration, estimation of the stagnation step, and optimizing the condition numbers of sensing matrices, are combined to improve the convergence speed. Both the ISAR imaging ability at low SNR and its speed are improved obviously. Finally, simulation experiments show that the proposed algorithm can shorten the imaging time and have better noise robustness under the condition of sub-Nyquist sampling rate and low SNR.

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.

Distributed ADMM for In-Network Reconstruction of Sparse Signals With Innovations

In this paper, we tackle the in-network recovery of sparse signals with innovations. We assume that the nodes of the network measure a signal composed by a common component and an innovation, both sparse and unknown, according to the joint sparsity model 1 (JSM-1). Acquisition is performed as in compressed sensing, hence the number of measurements is reduced. Our goal is to show that distributed algorithms based on the alternating direction method of multipliers (ADMM) can be efficient in this framework to recover both the common and the individual components. Specifically, we define a suitable functional and we show that ADMM can be implemented to minimize it in a distributed way, leveraging local communication between nodes. Moreover, we develop a second version of the algorithm, which requires only binary messaging, significantly reducing the transmission load.

Weighted multifeature hyperspectral image classification via kernel joint sparse representation

The advantage of using multifeature information for classification has been widely recognized. Representation-based methods with multifeature combination learning have only recently attracted increasing attention for hyperspectral classification. However, nonlinearity in data and the computational load of processing multifeature information and contextual information have been two thorny issues. In this paper, we present a fast joint sparse representation model with multifeature combination learning and its kernel extensions for hyperspectral imagery classification. For several complementary features (spectral, shape, and texture), the proposed model simultaneously acquires a representation vector for each type of feature and encourages the representation vectors to share a common sparsity pattern by imposing the joint sparsity ℓrow,0-norm regularization. Thus, the cross-feature information can be taken into account. For different features, different weights are assigned since they may not contribute equally to the final decision. Furthermore, kernel joint sparse representation model is presented to handle nonlinearity in the data. Kernel model projects the data into a high-dimensional space to improve the separability, achieving a better performance than the linear version. At the same time, we incorporate contextual neighborhood knowledge into the learned models. Experiments on several real hyperspectral images indicate that the proposed algorithms with much less memory requirements perform significantly faster than state-of-the-art algorithms, while exhibit highly competitive classification accuracy.

Joint Sparse Representation and Robust Feature-Level Fusion for Multi-Cue Visual Tracking.

Visual tracking using multiple features has been proved as a robust approach because features could complement each other. Since different types of variations such as illumination, occlusion, and pose may occur in a video sequence, especially long sequence videos, how to properly select and fuse appropriate features has become one of the key problems in this approach. To address this issue, this paper proposes a new joint sparse representation model for robust feature-level fusion. The proposed method dynamically removes unreliable features to be fused for tracking by using the advantages of sparse representation. In order to capture the non-linear similarity of features, we extend the proposed method into a general kernelized framework, which is able to perform feature fusion on various kernel spaces. As a result, robust tracking performance is obtained. Both the qualitative and quantitative experimental results on publicly available videos show that the proposed method outperforms both sparse representation-based and fusion based-trackers.

Hyperspectral Image Classification Based on Discriminative Joint Sparse Model and Label Refinement

Hyperspectral Image Classification Based on Discriminative Joint Sparse Model and Label Refinement

SAR Target Recognition via Joint Sparse Representation of Monogenic Signal

In this paper, the classification via sprepresentation and multitask learning is presented for target recognition in SAR image. To capture the characteristics of SAR image, a multidimensional generalization of the analytic signal, namely the monogenic signal, is employed. The original signal can be then orthogonally decomposed into three components: 1) local amplitude; 2) local phase; and 3) local orientation. Since the components represent the different kinds of information, it is beneficial by jointly considering them in a unifying framework. However, these components are infeasible to be directly utilized due to the high dimension and redundancy. To solve the problem, an intuitive idea is to define an augmented feature vector by concatenating the components. This strategy usually produces some information loss. To cover the shortage, this paper considers three components into different learning tasks, in which some common information can be shared. Specifically, the component-specific feature descriptor for each monogenic component is produced first. Inspired by the recent success of multitask learning, the resulting features are then fed into a joint sparse representation model to exploit the intercorrelation among multiple tasks. The inference is reached in terms of the total reconstruction error accumulated from all tasks. The novelty of this paper includes 1) the development of three component-specific feature descriptors; 2) the introduction of multitask learning into sparse representation model; 3) the numerical implementation of proposed method; and 4) extensive comparative experimental studies on MSTAR SAR dataset, including target recognition under standard operating conditions, as well as extended operating conditions, and the capability of outliers rejection.

Typical reconstruction limits for distributed compressed sensing based on ℓ2,1-norm minimization and Bayesian optimal reconstruction

The distributed compressed sensing framework provides an efficient compression scheme of multichannel signals that are sparse in some domains and highly correlated with one another. In particular, a signal model called the joint sparse model 2 (JSM-2) or multiple measurement vector problem, in which all sparse signals share their support, is important for dealing with practical problems such as magnetic resonance imaging and magnetoencephalography. In this paper, we investigate the typical reconstruction performance of JSM-2 problems for two schemes. One is ℓ2,1-norm minimization reconstruction and the other is Bayesian optimal reconstruction. Employing the replica method, we show that the reconstruction performance of both schemes which exploit the knowledge of the sharing of the signal support overcomes that of their corresponding approaches for the single-channel compressed sensing problem. We also develop a computationally feasible approximate algorithm for performing the Bayes optimal scheme to validate our theoretical estimation. Our replica-based analysis numerically indicates that the spinodal point of the Bayesian reconstruction disappears, which implies that a fundamental reconstruction limit can be achieved by the BP-based approximate algorithm in a practical amount of time when the number of channels is sufficiently large. The results of the numerical experiments of both reconstruction schemes agree excellently with the theoretical evaluation.

Multi-subspace pursuit algorithm based on body area network

Wireless body area networks (WBANs) provide a tremendous opportunity for remote health monitoring. However, the design of WBAN health monitoring system encounters a number of challenges including the process of the biomedical information. In this paper, we give an overview of the results of a special joint sparse model (JSM), JSM-2, in body area networks. We present JSM-2 for the signal groups that each signal has a common K-sparse characteristic although the biomedical signal groups are not all sparse signals. The reconstruction algorithm, multi-subspace pursuit algorithm, is proposed based on JSM-2. The algorithm combines the advantages of the previous study of the one-step greedy algorithm (OSGA) and simultaneous orthogonal matching pursuit (SOMP). Furthermore, the proposed algorithm not only performs better in sparse reconstruction performance than OSGA, but also needs less calculation than SOMP. The performance is evaluated through numerical simulations.

Enhancing gait based person identification using joint sparsity model and [formula omitted]-norm minimization

We consider the problem of person identification using gait sequences under normal, carrying bag and different clothing conditions as the main concern. It has been demonstrated that Gait Energy Image (GEI) can attain a better gait recognition rate under normal conditions. However, it has been shown that GEI is not robust enough to handle the carrying bags and different clothing conditions. Instead of GEI, there are several appearance based gait features in the available literature to reduce the effect of covariate factors by keeping dynamic parts and removing the static parts of the gait features under the assumption that the carrying bags and different clothing conditions affect mostly the static parts. It is however shown in the literature that the static parts also contain valuable information and removal of certain static parts such as head by mistake thigh typed certainly decreases the recognition rate.Our main objective has been to increase the gait recognition rate on different clothing and carrying bag covariate gait sequences. Therefore instead of removing static parts, the Joint Sparsity Model (JSM) is applied to identify the carrying bags and different clothings conditions from GEI features. If a set of GEI feature vectors is submitted to JSM model then a common component and an innovations component for each GEI feature are obtained. The innovations component that has unique characteristic to each of features is considered to identify the covariate conditions. The identified covariate conditions are removed from GEI features and a novel gait feature called GEIJSM is generated. The dimension of GEIJSM is reduced using Random Projection (RP) approach and ℓ1-norm minimization technique based sparse representation is used for classification. It is demonstrated that the RP and ℓ1-norm minimization based sparse representation approach provides statistically significant better results than that of the existing individual identification approaches.