Joint Sparse Model Research Articles

Random subspace based ensemble sparse representation

In this paper, a new random subspace based ensemble sparse representation (RS_ESR) algorithm is proposed, where the random subspace is introduced into sparse representation model. For high-dimensional data, the random subspace method can not only reduce dimension of data but also make full use of effective information of data. It is not like traditional dimensionality reduction methods that may lose some information of original data. Additionally, a joint sparse representation model is emloyed to obtain the sparse representation of a sample set in the low dimensional random subspace. Then the sparse representations in multiple random subspaces are integrated as an ensemble sparse representation. Moreover, the obtained RS_ESR is applied in classical clustering and semi-supervised classification. The experimental results on different real-world data sets show the superiority of RS_ESR over traditional methods.

Look-Ahead Hybrid Matching Pursuit for Multipolarization Through-Wall Radar Imaging

In this paper, we propose a novel greedy algorithm referred to as look-ahead hybrid matching pursuit (LAHMP) for multipolarization through-wall radar imaging (TWRI). From the viewpoint of compressive sensing, the task of multipolarization TWRI can be formulated as a problem of sparsity pattern recovery under the joint sparsity model. A newly developed greedy algorithm for joint sparsity model, hybrid matching pursuit (HMP), combines the strengths of orthogonal matching pursuit and subspace pursuit and improves the accuracy of the sparsity pattern recovery. Besides, the look-ahead strategy can select an optimal atom by evaluating its effectiveness on the overall reconstruction quality. Through integrating the virtues of HMP with the look-ahead strategy, the proposed LAHMP aims to more accurately select atoms corresponding to the true targets behind walls. Experiments based on measured radar data show that, compared to existing greedy algorithms, LAHMP provides better image quality at affordable expense of computational complexity.

Enhanced joint sparsity via iterative support detection

Joint sparsity has attracted considerable attention in recent years in many fields including sparse signal recovery in compressive sensing, statistics, and machine learning. Traditional convex models with joint sparsity suffer from the suboptimal performance though enjoying tractable computation. In this paper, we propose a new non-convex joint sparsity model, and develop a corresponding multi-stage adaptive convex relaxation algorithm. This method extends the idea of iterative support detection (ISD) from the single vector estimation to the multi-vector estimation by considering the joint sparsity prior. We provide some preliminary theoretical analysis including convergence analysis and a sufficient recovery condition. Numerical experiments from both compressive sensing and multi-task feature learning show the better performance of the proposed method in comparison with several state-of-the-art alternatives. Moreover, we demonstrate that the extension of ISD from the single vector to multi-vector estimation is not trivial. While ISD does not well reconstruct the single channel sparse Bernoulli signal, it does achieve significantly improved performance when recovering the multi-channel sparse Bernoulli signal thanks to its ability of natural incorporation of the joint sparsity structure.

Multi-Feature Joint Sparse Model for the Classification of Mangrove Remote Sensing Images

Mangroves are valuable contributors to coastal ecosystems, and remote sensing is an indispensable way to obtain knowledge of the dynamics of mangrove ecosystems. Due to the similar spectral features between mangroves and other land cover types, challenges are posed since the accuracy is sometimes unsatisfactory in distinguishing mangroves from other land cover types with traditional classification methods. In this paper, we propose a classification method named the multi-feature joint sparse algorithm (MF-SRU), in which spectral, topographic, and textural features are integrated as the decision-making features, and sparse representation of both center pixels and their eight neighborhood pixels is proposed to represent the spatial correlation of neighboring pixels, which can make good use of the spatial correlation of adjacent pixels. Experiments are performed on Landsat Thematic Mapper multispectral remote sensing imagery in the Zhangjiang estuary in Southeastern China, and the results show that the proposed method can effectively improve the extraction accuracy of mangroves.

Adaptive Grouping Distributed Compressive Sensing Reconstruction of Plant Hyperspectral Data.

With the development of hyperspectral technology, to establish an effective spectral data compressive reconstruction method that can improve data storage, transmission, and maintaining spectral information is critical for quantitative remote sensing research and application in vegetation. The spectral adaptive grouping distributed compressive sensing (AGDCS) algorithm is proposed, which enables a distributed compressed sensing reconstruction of plant hyperspectral data. The spectral characteristics of hyperspectral data are analyzed and the joint sparse model is constructed. The spectral bands are adaptively grouped and the hyperspectral data are compressed and reconstructed on the basis of grouping. The experimental results showed that, compared with orthogonal matching pursuit (OMP) and gradient projection for sparse reconstruction (GPSR), AGDCS can significantly improve the visual effect of image reconstruction in the spatial domain. The peak signal-to-noise ratio (PSNR) at a low sampling rate (the sampling rate is lower than 0.2) increases by 13.72 dB than OMP and 1.66 dB than GPSR. In the spectral domain, the average normalized root mean square error, the mean absolute percentage error, and the mean absolute error of AGDCS is 35.38%, 31.83%, and 33.33% lower than GPSR, respectively. Additionally, AGDCS can achieve relatively high reconstructed efficiency.

Space target image fusion method based on image clarity criterion

Optical and infrared imaging is often used in ground-based optical space target observation. The fusion of the two types of images for a more detailed observation is the key problem to be solved. A space target multimodal image fusion scheme based on the joint sparsity model, which takes the correlations among the native sparse characteristics of the image, clarity features of the image, and multisource images into consideration, is proposed. First, using an overcomplete dictionary, the source images are represented as a combination of a shared sparse component and exclusive sparse components. Second, a method for image clarity feature extraction is proposed to design the fusion rules of exclusive sparse components to obtain the fused exclusive sparse components. Finally, the fused image is reconstructed with the fused sparse components and overcompleted dictionary. The proposed method was tested on the space target image and nature scene image data sets. Compared with traditional methods such as the multiscale transform-based methods, sparse representation-based methods, and joint sparsity representation-based methods, the final experimental results demonstrated that our method outperforms the existing state-of-the-art methods on the human visual effect and the objective evaluation indexes. In particular, for the evaluation indexes Q A B / F and Q E , the scores increase to nearly 10% more than those for traditional methods, which indicates that the fused image of our method has better edge clarity.

An Efficient Distributed Compressed Sensing Algorithm for Decentralized Sensor Network.

We consider the joint sparsity Model 1 (JSM-1) in a decentralized scenario, where a number of sensors are connected through a network and there is no fusion center. A novel algorithm, named distributed compact sensing matrix pursuit (DCSMP), is proposed to exploit the computational and communication capabilities of the sensor nodes. In contrast to the conventional distributed compressed sensing algorithms adopting a random sensing matrix, the proposed algorithm focuses on the deterministic sensing matrices built directly on the real acquisition systems. The proposed DCSMP algorithm can be divided into two independent parts, the common and innovation support set estimation processes. The goal of the common support set estimation process is to obtain an estimated common support set by fusing the candidate support set information from an individual node and its neighboring nodes. In the following innovation support set estimation process, the measurement vector is projected into a subspace that is perpendicular to the subspace spanned by the columns indexed by the estimated common support set, to remove the impact of the estimated common support set. We can then search the innovation support set using an orthogonal matching pursuit (OMP) algorithm based on the projected measurement vector and projected sensing matrix. In the proposed DCSMP algorithm, the process of estimating the common component/support set is decoupled with that of estimating the innovation component/support set. Thus, the inaccurately estimated common support set will have no impact on estimating the innovation support set. It is proven that under the condition the estimated common support set contains the true common support set, the proposed algorithm can find the true innovation set correctly. Moreover, since the innovation support set estimation process is independent of the common support set estimation process, there is no requirement for the cardinality of both sets; thus, the proposed DCSMP algorithm is capable of tackling the unknown sparsity problem successfully.

Composite SAR imaging using sequential joint sparsity

This paper investigates accurate and efficient ℓ1 regularization methods for generating synthetic aperture radar (SAR) images. Although ℓ1 regularization algorithms are already employed in SAR imaging, practical and efficient implementation in terms of real time imaging remain a challenge. Here we demonstrate that fast numerical operators can be used to robustly implement ℓ1 regularization methods that are as or more efficient than traditional approaches such as back projection, while providing superior image quality. In particular, we develop a sequential joint sparsity model for composite SAR imaging which naturally combines the joint sparsity methodology with composite SAR. Our technique, which can be implemented using standard, fractional, or higher order total variation regularization, is able to reduce the effects of speckle and other noisy artifacts with little additional computational cost. Finally we show that generalizing total variation regularization to non-integer and higher orders provides improved flexibility and robustness for SAR imaging.

Hyperspectral image classification based on joint sparsity model with low-dimensional spectral–spatial features

We propose a hyperspectral image (HSI) classification method combining low-dimensional spectral–spatial features with joint sparsity model (JSM). First, for the high-dimensional data sets, we introduced image fusion for feature reduction. Then fast bilateral filtering is adopted to exploit spatial features, which will be combined with the original spectral features for classification. Based on the low-dimensional spectral–spatial features, we utilize JSM to serve as a classifier. Considering the strong relationship between the neighboring pixels in HSI, this model can achieve a promising performance by exploiting regional spectral–spatial information. Overall accuracies (with 10% and 2% training samples) of the proposed method are 97.84% and 97.52% for the Indian Pines image and University of Pavia image. Experimental results on different HSI data sets show that the proposed method shows outstanding performance in terms of classification accuracy and computational efficiency.

Block compressive sensing: Individual and joint reconstruction of correlated images

Compressive sensing provides simultaneous sensing and compression of data. Block compressive sensing (BCS) of images has gained a prominence in recent years due to low encoding complexity. In this paper, we propose the reconstruction algorithm for BCS framework based on iterative re-weighted l1 norm minimization. In the proposed algorithm, the desired signal sparsity is achieved using l1 norm minimization while Wiener filtering is incorporated as the smoothing operator. We also propose block based joint reconstruction algorithm for correlated images and video frames. The correlation is captured through the joint sparsity model by minimizing the objective function which promotes the common sparsity structure. The performance of proposed algorithms is tested on different stereo images and video data. Our analysis shows that the proposed individual reconstruction algorithm gives good compression performance as compared to existing schemes. Extensive analysis on correlated images demonstrates that the proposed joint reconstruction algorithm outperforms individual reconstruction algorithms.

Multiple Kernel Sparse Representation for Airborne LiDAR Data Classification

To effectively learn heterogeneous features extracted from raw LiDAR point cloud data for landcover classification, a multiple kernel sparse representation classification (MKSRC) framework is proposed in this paper. In the MKSRC, multiple kernel learning (MKL) is embedded into sparse representation classification (SRC). The heterogeneous features are first extracted from the raw LiDAR point cloud data before classification. These features contain useful information from different dimensions, including single point features and neighbor features. Based on feature extraction, on the one hand, MKL is reasonably integrated into the SRC, namely, different base kernels that are constructed with each heterogeneous feature separately are utilized in the process of sparse representation. Furthermore, joint sparsity model is also introduced into the MKSRC framework and multiple kernel joint SRC (MKJSRC) is then proposed. On the other hand, improved kernel alignment (IKA) methods are proposed to more effectively determine the weights of base kernels in both of MKSRC and MKJSRC. Experiments are conducted on three real airborne LiDAR data sets. The experimental results demonstrate that MKSRC and MKJSRC frameworks can effectively learn the heterogeneous features for LiDAR point cloud classification and outperforms the other state-of-the-art sparse representation-based classifiers and the recent MKL algorithm. Moreover, the proposed IKA is helpful to better determine the “optimal” weights of the base kernels in both MKSRC and MKJSRC than in the existing kernel alignment method.

Identifiability in Bilinear Inverse Problems With Applications to Subspace or Sparsity-Constrained Blind Gain and Phase Calibration

Bilinear inverse problems (BIPs), the resolution of two vectors given their image under a bilinear mapping, arise in many applications. Without further constraints, BIPs are usually ill-posed. In practice, the properties of natural signals are exploited to solve BIPs. For example, subspace constraints or sparsity constraints are imposed to reduce the search space. These approaches have shown some success in practice. However, there are few results on uniqueness in BIPs. For most BIPs, the fundamental question of under what condition the problem admits a unique solution is yet to be answered. For example, blind gain and phase calibration (BGPC) is a structured BIP, which arises in many applications, including inverse rendering in computational relighting (albedo estimation with unknown lighting), blind phase and gain calibration in sensor array processing, and multichannel blind deconvolution (MBD). It is interesting to study the uniqueness of such problems. In this paper, we define identifiability of a BIP up to a group of transformations. We derive necessary and sufficient conditions for such identifiability, i.e., the conditions under which the solutions can be uniquely determined up to the transformation group. These conditions take the form of dividing the identifiability of the pair of unknown variables into the individual identifiability of each variable. Although verifying these individual conditions requires problem-specific procedures, this framework is universally applicable to all BIPs. Applying these results to BGPC, we derive sufficient conditions for unique recovery under several scenarios, including subspace, joint sparsity, and sparsity models. For BGPC with joint sparsity or sparsity constraints, we develop a procedure to compute the transformation groups corresponding to inherent ambiguities. We also give necessary conditions in the form of tight lower bounds on sample complexities, and demonstrate the tightness of these bounds by numerical experiments. The results for BGPC not only demonstrate the application of the proposed general framework for identifiability analysis, but are also of interest in their own right.

Joint-2D-SL0 Algorithm for Joint Sparse Matrix Reconstruction

Sparse matrix reconstruction has a wide application such as DOA estimation and STAP. However, its performance is usually restricted by the grid mismatch problem. In this paper, we revise the sparse matrix reconstruction model and propose the joint sparse matrix reconstruction model based on one-order Taylor expansion. And it can overcome the grid mismatch problem. Then, we put forward the Joint-2D-SL0 algorithm which can solve the joint sparse matrix reconstruction problem efficiently. Compared with the Kronecker compressive sensing method, our proposed method has a higher computational efficiency and acceptable reconstruction accuracy. Finally, simulation results validate the superiority of the proposed method.

Multi-Task Joint Sparse and Low-Rank Representation for the Scene Classification of High-Resolution Remote Sensing Image

Scene classification plays an important role in the intelligent processing of High-Resolution Satellite (HRS) remotely sensed images. In HRS image classification, multiple features, e.g., shape, color, and texture features, are employed to represent scenes from different perspectives. Accordingly, effective integration of multiple features always results in better performance compared to methods based on a single feature in the interpretation of HRS images. In this paper, we introduce a multi-task joint sparse and low-rank representation model to combine the strength of multiple features for HRS image interpretation. Specifically, a multi-task learning formulation is applied to simultaneously consider sparse and low-rank structures across multiple tasks. The proposed model is optimized as a non-smooth convex optimization problem using an accelerated proximal gradient method. Experiments on two public scene classification datasets demonstrate that the proposed method achieves remarkable performance and improves upon the state-of-art methods in respective applications.

Increasing Axial Resolution of Ultrasonic Imaging With a Joint Sparse Representation Model.

The axial resolution of ultrasonic imaging is confined by the temporal width of acoustic pulse generated by the transducer, which has a limited bandwidth. Deconvolution can eliminate this effect and, therefore, improve the resolution. However, most ultrasonic imaging methods perform deconvolution scan line by scan line, and therefore the information embedded within the neighbor scan lines is unexplored, especially for those materials with layered structures such as blood vessels. In this paper, a joint sparse representation model is proposed to increase the axial resolution of ultrasonic imaging. The proposed model combines the sparse deconvolution along the axial direction with a sparsity-favoring constraint along the lateral direction. Since the constraint explores the information embedded within neighbor scan lines by connecting nearby pixels in the ultrasound image, the axial resolution of the image improves after deconvolution. The results on simulated data showed that the proposed method can increase resolution and discover layered structure. Moreover, the results on real data showed that the proposed method can measure carotid intima-media thickness automatically with good quality ( 0.56±0.03 versus 0.60±0.06 mm manually).

Joint sparse model-based discriminative K-SVD for hyperspectral image classification

Sparse representation classification (SRC) is being widely investigated on hyperspectral images (HSI). For SRC methods to achieve high classification performance, not only is the development of sparse representation models essential, the designing and learning of quality dictionaries also plays an important role. That is, a redundant dictionary with well-designated atoms is required in order to ensure low reconstruction error, high discriminative power, and stable sparsity. In this paper, we propose a new method to learn such dictionaries for HSI classification. We borrow the concept of joint sparse model (JSM) from SRC to dictionary learning. JSM assumes local smoothness and joint sparsity and was initially proposed for classification of HSI. We leverage JSM to develop an extension of discriminative K-SVD for learning a promising discriminative dictionary for HSI. Through a semi-supervised strategy, the new dictionary learning method, termed JSM-DKSVD, utilises all spectrums over the local neighbourhoods of labelled training pixels for discriminative dictionary learning. It can produce a redundant dictionary with rich spectral and spatial information as well as high discriminative power. The learned dictionary can then be compatibly used in conjunction with the established SRC methods, and can significantly improve their performance for HSI classification.

Texture clear multi-modal image fusion with joint sparsity model

Multi-modal image fusion is necessary for describing a target abundantly. With the consideration of the correlations between multi-source signals and the sparse characteristics of image, this paper proposed a novel fusion rule of multi-modal image fusion scheme based on the joint sparsity model. First, the source image was represented as a shared sparse component and an exclusive sparse component with an over-complete dictionary. Second, the designed novel fusion rule acts on the shared and exclusive sparse coefficients to obtain the fused sparse coefficients. Finally, fused image was reconstructed by the fused sparse coefficients and the dictionary. The proposed approach was tested on the infrared and visual images, medical images. The results were compared with those of traditional methods, such as the multi-scale transform based methods, sparse representation based methods and joint sparsity representation based methods. Experimental results demonstrated that the proposed method outperforms the existing state-of-the-art methods, in terms of better texture clarity. Moreover, the fused image shows better edge consistence and visual effect.

Optimal Sample Complexity for Blind Gain and Phase Calibration

Blind gain and phase calibration (BGPC) is a structured bilinear inverse problem, which arises in many applications, including inverse rendering in computational relighting (albedo estimation with unknown lighting), blind phase and gain calibration in sensor array processing, and multichannel blind deconvolution. The fundamental question of the uniqueness of the solutions to such problems has been addressed only recently. In a previous paper, we proposed studying the identifiability in bilinear inverse problems up to transformation groups. In particular, we studied several special cases of blind gain and phase calibration, including the cases of subspace and joint sparsity models on the signals, and gave sufficient and necessary conditions for identifiability up to certain transformation groups. However, there were gaps between the sample complexities in the sufficient conditions and the necessary conditions. In this paper, under a mild assumption that the signals and models are generic, we bridge the gaps by deriving tight sufficient conditions with optimal sample complexities.

Exploiting joint sparsity for underwater acoustic MIMO communications

MIMO communication has been recognized as a potential solution for high speed underwater acoustic communication, which unfortunately encounters significant difficulties posed by simultaneous presence of multipath and Co-channel interference (CoI). Sparsity contained in the multipath structure of underwater acoustic channels offers an effective way for improving channel estimation quality and thus enhancing the communication performance in the form of time reversal or channel estimation based equalization. However, for MIMO channels with extensive multipath and CoI, the performance gain achieved by classic sparsity exploitation channel estimation methods such as orthogonal matching pursuit (OMP) is still not enough to yield satisfactory performance. Under quasi-stationary assumption, underwater acoustic channels of adjacent data blocks exhibit correlated multipath structure, namely, multipath arrivals with similar time delay but different magnitude, which has not been exploited. In this paper, a joint sparse recovery approach is proposed to exploit the sparse correlation among adjacent data blocks to improve the performance of channel estimation. Under the framework of distributed compressed sensing (DCS), a joint sparse model which treats the multipath arrivals as sparse solutions with common time support is adopted to derive a joint sparse recovery algorithm for efficient channel estimation, the results of which are used to initialize and periodly update a channel estimation based time reversal receiver. Finally, underwater MIMO communication experimental results obtained in a shallow water channel are provided to demonstrate the effectiveness of the proposed method, compared to the same type of receiver that do not exploit the joint sparse.

A brief introduction to distributed compressed sensing and its typical reconstruction limits

A brief introduction to compressed sensing and a discussion of its reconstruction limit analysis are presented. In addition, we briefly introduce the replica method, a technique in statistical mechanics, to show its effectiveness for typical performance analysis on signal processing problems. In this presentation, we especially focus on a signal model called joint sparse model 2 (JSM-2) or the multiple measurement vector problem, in which all sparse signals share their support. The signal model JSM-2 is important for dealing with practical processing problems. We investigate the typical performance of l2,1-norm regularized minimization and the Bayesian optimal reconstruction schemes in terms of mean square error for noiseless and noisy measurement JSM- 2 problems. Employing the replica method, we show that these schemes, which exploit the knowledge that the signal support is shared, can recover the signals more precisely as the number of channels increases. The main focus of our presentation is theoretical analysis; however, we will introduce applications of the signal model JSM-2 for acoustic problems. Most of our presentation is based on papers J. Stat. Mech. (2015) P05029 and J. Stat. Mech. (2016) 063304.