Sparse Representation Framework Research Articles

Robust detection of neural spikes using sparse coding based features.

The detection of neural spikes plays an important role in studying and processing extracellular recording signals, which promises to be able to extract the necessary spike data for all subsequent analyses. The existing algorithms for spike detection have achieved great progress but there still remains much room for improvement in terms of the robustness to noise and the flexibility in the spike shape. To address this issue, this paper presents a novel method for spike detection based on the theory of sparse representation. By analyzing the characteristics of extracellular neural recordings, a targetdriven sparse representation framework is firstly constructed, with which the neural spike signals can be effectively separated from background noise. In addition, considering the fact that the spikes emitted by different neurons have different shapes, we then learn a universal dictionary to give a sparse representation of various spike signals. Finally, the information (location and number) of spikes in the recorded signal are achieved by comprehensively analyzing the sparse features. Experimental results demonstrate that the proposed method outperforms the existing methods in the spike detection problem.

Refocusing of Moving Targets Based on Low-Bit Quantized SAR Data via Parametric Quantized Iterative Hard Thresholding

Low-bit quantization of echo improves storage and leads to more efficient downlink transmission of spaceborne synthetic aperture radar (SAR) systems. In this paper, a new parametric quantized iterative hard thresholding (PQIHT) algorithm is proposed to refocus the images of moving targets with low-bit quantized SAR data, based on the combination of quantized iterative hard thresholding (QIHT) and the parametric sparse representation. The blurred and quantization-error-involved subimage of the region of interest (ROI) containing the moving target is represented in a sparse fashion through an adaptive parametric dictionary. The QIHT with a pruned searching method is performed for efficiently estimating the motion-adaptive parameter inside the dictionary, refocusing the ROI image and suppressing the quantization-induced error in an iterative way. Different from the conventional QIHT algorithm with a fixed dictionary that can only represent stationary targets, the proposed method exploits a parametric dictionary with a parameter related to target motion status, which is capable of adaptively representing the radar echo from a moving target with unknown motion status and, therefore, is suitable for moving target refocusing. Simulations and experiments on real GF-3 satellite SAR data demonstrate that, compared with the conventional parametric sparse representation framework for moving target refocusing based on purely precise data, the proposed algorithm can provide satisfactory quality of moving target refocusing with remarkably reduced data volume.

Modal regression based greedy algorithm for robust sparse signal recovery, clustering and classification

Greedy algorithm (GA) is an efficient sparse representation framework with numerous applications in machine learning and computer vision. However, conventional GA methods may fail when applied to grossly corrupted data because they iteratively estimate the sparse signal using least squares regression, which is sensitive to gross corruption and outliers. In this paper, we propose a modal regression based greedy algorithm referred as MROMP (modal regression based orthogonal matching pursuit) to robustly learn the sparse signal from corrupted measurements. Unlike previous GA methods, MROMP is based on sparse modal regression, which has decent robustness to heavy-tailed noise and outliers. To efficiently optimize MROMP, we devise two half-quadratic based algorithms with guaranteed convergence. Our another two contributions are leveraging MROMP to develop a robust subspace clustering method to cluster data lying in a union of subspaces, and a robust pattern classification method to recognize data into the class that they belong to, respectively. The experimental results on both simulated and real datasets demonstrate the efficacy and robustness of MROMP for sparse signal recovery, data clustering and classification, especially for grossly corrupted data.

A new sparse representation framework for compressed sensing MRI

Compressed sensing based Magnetic Resonance imaging (MRI) via sparse representation (or transform) has recently attracted broad interest. The tight frame (TF)-based sparse representation is a promising approach in compressed sensing MRI. However, the conventional TF-based sparse representation is difficult to utilize the sparsity of the whole image. Since the whole image usually has different structure textures and a kind of tight frame can only represent a particular kind of ground object, how to reconstruct high-quality of magnetic resonance (MR) image is a challenge. In this work, we propose a new sparse representation framework, which fuses the double tight frame (DTF) into the mixed-norm regularization for MR image reconstruction from undersampled k-space data. In this framework, MR image is decomposed into smooth and nonsmooth regions. For the smooth regions, the wavelet TF-based weighted L1-norm regularization is developed to reconstruct piecewise-smooth information of image. For nonsmooth regions, we introduce the curvelet TF-based robust L1,a-norm regularization with the parameter to preserve the edge structural details and texture. To estimate the reasonable parameter, an adaptive parameter selection scheme is designed in robust L1,a-norm regularization. Experimental results demonstrate that the proposed method can achieve the best image reconstruction results when compared with other existing methods in terms of quantitative metrics and visual effect.

Low-rank local tangent space embedding for subspace clustering

Subspace techniques have gained much attention for their remarkable efficiency in representing high-dimensional data, in which sparse subspace clustering (SSC) and low-rank representation (LRR) are two commonly used prototypes in the fields of pattern recognition, computer vision and signal processing. Both of them aim at constructing a block sparse matrix via linearly representing data to make them be embedded into linear subspaces. However, few datasets satisfy the linear subspace assumption in the real world. In this paper, data are peered from viewpoint of manifold architecture under the framework of sparse representation. A globally low-rank representation with the Frobenius norm minimization is constructed under the constraint of local manifold embedding and a novel low-rank local embedding representation (LRLER) model for subspace clustering of datasets is proposed. In this model, the local as well as global manifold structures of a dataset are concerned. Clusters of a dataset are considered as sub-manifolds embedded in low-dimensional subspaces. To represent and segment samples with hybrid neighbors or interlaced manifold structures, the local tangent space analysis strategy is introduced to characterize the local structure of neighborhood of samples. The coefficients of locally linear embedding are rectified according to the relationship between local tangent spaces of samples and their neighbors. A local tangent space based low-rank local embedding representation model (LRLTSER) is built to deal with data with neighborhood aliasing distortion. Extensive experiments on synthetic datasets and real-world datasets are implemented and experimental results show superior performance of the proposed methods for subspace clustering compared to the state-of-the-art techniques.

An Effective Algorithm for Single Image Fog Removal

Poor visibility due to the effects of light absorption and scattering is challenging for processing images captured in foggy weather conditions. This paper proposes an effective algorithm for single image fog removal based on degradation model and group-based sparse representation (GSR). The proposed degradation model is constructed based on a classical physical model, i.e., dichromatic atmospheric scattering model. Then, the new degradation model is integrated into the group-based sparse representation framework. Finally, the single image defogging problem is regarded as an image restoration problem, which can be well optimized by GSR. The method is compared with several well-known algorithms from the literature using qualitative and quantitative evaluations, and results indicate considerable improvement over existing algorithms.

Wavelet based dictionaries for dimensionality reduction of ECG signals

Dimensionality reduction of ECG signals is considered within the framework of sparse representation. The approach constructs the signal model by selecting elementary components from a redundant dictionary via a greedy strategy. The proposed wavelet dictionaries are built from the multiresolution scheme, but translating the prototypes within a shorter step than that corresponding to the wavelet basis. The reduced representation of the signal is shown to be suitable for compression at low level distortion. In that regard, compression results are superior to previously reported benchmarks on the MIT-BIH Arrhythmia data set.

Robust auto-weighted projective low-rank and sparse recovery for visual representation

Most existing low-rank and sparse representation models cannot preserve the local manifold structures of samples adaptively, or separate the locality preservation from the coding process, which may result in the decreased performance. In this paper, we propose an inductive Robust Auto-weighted Low-Rank and Sparse Representation (RALSR) framework by joint feature embedding for the salient feature extraction of high-dimensional data. Technically, the model of our RALSR seamlessly integrates the joint low-rank and sparse recovery with robust salient feature extraction. Specifically, RALSR integrates the adaptive locality preserving weighting, joint low-rank/sparse representation and the robustness-promoting representation into a unified model. For accurate similarity measure, RALSR computes the adaptive weights by minimizing the joint reconstruction errors over the recovered clean data and salient features simultaneously, where L1-norm is also applied to ensure the sparse properties of learnt weights. The joint minimization can also potentially enable the weight matrix to have the power to remove noise and unfavorable features by reconstruction adaptively. The underlying projection is encoded by a joint low-rank and sparse regularization, which can ensure it to be powerful for salient feature extraction. Thus, the calculated low-rank sparse features of high-dimensional data would be more accurate for the subsequent classification. Visual and numerical comparison results demonstrate the effectiveness of our RALSR for data representation and classification.

Hybrid approach for ECG signal enhancement using dictionary learning‐based sparse representation

Electrocardiogram (ECG) signal quality enhancement is a crucial task in the computer-based automated processing system. In this study, a dictionary learning (DL)-based sparse representation framework is presented for ECG signal enhancement through denoising. Unlike, traditional filtering techniques, the proposed method removes both low- and high-frequency noises for complete enhancement of the signal quality. The frequency localised DL-based sparse representation approach is applied to remove both baseline wander and power-line interference. The time-localised and signal characteristics based DL-based sparse representation scheme is employed for extraction of clean ECG components from white Gaussian noise and muscle artefact added noisy ECG record. Both qualitative and quantitative performance analyses are carried out using the Massachusetts Institute of Technology - Beth Israel Hospital (MIT-BIH) database, QT database and synthetic ECG signals. The efficacy of the proposed method is compared with the existing ECG denoising approaches using standard performance metrics: signal-to-noise ratio, root-mean-square error and percentage RMS difference. It is observed through the detailed study and analysis that the proposed approach outperforms the existing ones and can be served to further enhance the overall quality of ECG in a computer-based automated medical system.

A graphical estimation and multiple-sparse representation strategy for hyperspectral anomaly detection

Most hyperspectral anomaly detection (AD) methods only utilize spectral information in hyperspectral images (HSI) to distinguish anomaly targets from backgrounds. However, the features extracted by spectral difference are incomplete and will limit the performance of AD. To overcome the drawbacks and obtain abundant feature information of diverse components, we propose a novel hyperspectral AD strategy based on graphical estimation and multiple-sparse representation. First, the potential anomalies can be screened out by a prior graphical connected region (PGCR) estimation, by which the potential anomalies are distinguished from robust background spatially. Second, based on sparse representation (SR) theory, a multiple SR framework is utilized to select spectral feature information. It can pick out the representative spectra that further enlarge anomaly’s distinction from background. Consequently, a fusion strategy is designed to comprehensively determine different groups of results generated by multiple SR method and to obtain the final detection result. In the experiment, the proposed method achieves a more superior result than other classic or popular AD detectors. A detailed analysis of the relevant parameters and their sensitivity under specific condition are also discussed in the experimental section.

An integrated inverse space sparse representation framework for tumor classification

Microarray gene expression data-based tumor classification is an active and challenging issue. In this paper, an integrated tumor classification framework is presented, which aims to exploit information in existing available samples, and focuses on the small sample problem and unbalanced classification problem. Firstly, an inverse space sparse representation based classification (ISSRC) model is proposed by considering the characteristics of gene-based tumor data, such as sparsity and a small number of training samples. A decision information factors (DIF)-based gene selection method is constructed to enhance the representation ability of the ISSRC. It is worth noting that the DIF is established from reducing clinical misdiagnosis rate and dimension of small sample data. For further improving the representation ability and classification stability of the ISSRC, feature learning is conducted on the selected gene subset. The feature learning method is constructed by complementing the advantages of non-negative matrix factorization (NMF) and deep learning. Without confusion, the ISSRC combined with gene selection and feature learning is called the integrated ISSRC, whose stability, optimization and the corresponding convergence are analyzed. Extensive experiments on six public microarray gene expression datasets show the integrated ISSRC-based tumor classification framework is superior to classical and state-of-the-art methods. There are significant improvements in classification accuracy, specificity and sensitivity, whether there is a tumor in the early diagnosis, what kind of tumor, or whether metastasis occurs after tumor surgery.

Correlation-Weighted Sparse Representation for Robust Liver DCE-MRI Decomposition Registration.

Conducting an accurate motion correction of liver dynamic contrast-enhanced magnetic resonance (DCE-MR) imaging remains challenging because of intensity variations caused by contrast agents. Such variations lead to the failure of the traditional intensity-based registration method. To address this problem, we propose a correlation-weighted sparse representation framework to separate the contrast agent from original liver DCE-MR images. This framework allows the robust registration of motion components over time without intensity variances. Existing sparse coding techniques recover a 3D image containing only contrast agents (named contrast enhancement component) from a manually labeled dictionary, whose column has the same size with the original 3D volume (3D-t mode). The high dimension of the recovery target (3D volume) and the indistinguishability between the unenhanced and enhanced images make accurate coding difficult. In this paper, we predefine an ideal time-intensity curve containing only contrast agents (named contrast agent curve) and recover it from the transpose dictionary (t-3D mode), whose column has been updated into the original time-intensity curves. The low dimension of the target (1D curve) and the significant intergroup difference between contrast agent curves and non-contrast agent curves can estimate a series of pure contrast agent curves. A "correlation-weighted" constraint is introduced for the selection of a coding subset with more contrast agent curves, leading to an efficient and accurate sparse recovery process. Then, the contrast enhancement component can be estimated by the solved sparse coefficients' map and the ideal curve and subtracted from the original DCE-MRI. Finally, we register the de-enhanced images and apply the obtained deformation fields for the original DCE-MRI to achieve the goal of motion correction. We conduct the experiments on both simulated and real liver DCE-MRI data. Compared with other state-of-the-art DCE-MRI registration methods, the experimental results show that our method achieves a better registration performance with less computational efficiency.

Superpixel based Feature Specific Sparse Representation for Spectral-Spatial Classification of Hyperspectral Images

To improve the performance of the sparse representation classification (SRC), we propose a superpixel-based feature specific sparse representation framework (SPFS-SRC) for spectral-spatial classification of hyperspectral images (HSI) at superpixel level. First, the HSI is divided into different spatial regions, each region is shape- and size-adapted and considered as a superpixel. For each superpixel, it contains a number of pixels with similar spectral characteristic. Since the utilization of multiple features in HSI classification has been proved to be an effective strategy, we have generated both spatial and spectral features for each superpixel. By assuming that all the pixels in a superpixel belongs to one certain class, a kernel SRC is introduced to the classification of HSI. In the SRC framework, we have employed a metric learning strategy to exploit the commonalities of different features. Experimental results on two popular HSI datasets have demonstrated the efficacy of our proposed methodology.

Reconstruction From Multispectral to Hyperspectral Image Using Spectral Library-Based Dictionary Learning

High-spatial hyperspectral (HH) image reconstruction using both high-spatial multispectral (HM) image and low-spatial hyperspectral (LH) image over the same scene is widely used in many real applications. Nevertheless, the pair of HM image and LH image over the same scene is hard to obtain. To solve this problem, a new HH image reconstruction method using spectral library-based dictionary learning (named as HIRSL) is proposed in this paper, only from one HM image. The above reconstruction problem is formulated in the framework of sparse representation, as an estimation of the band matching matrix, the spectral dictionary, and the sparse coefficients. More specifically, a band matching method is proposed for mapping the common spectral library to a specific spectral library corresponding to the reconstructed HH image in spectral domain. Then, an efficient spectral dictionary learning method is proposed for the construction of spectral dictionary using the matched specific spectral library, which avoids the dependence of the LH image over the same scene. Finally, the sparse coefficients of the HM image with respect to the learned spectral dictionary are estimated using the alternating direction method of multipliers without nonnegative constraint. Comparison results on simulated and real data sets with the relative state-of-the-art methods demonstrate that even only using one HM image, our proposed method achieves a comparable reconstruction quality of high-spatial hyperspectral image both in spatial and spectral domains.

Weighted graph regularized sparse brain network construction for MCI identification

Brain functional networks (BFNs) constructed from resting-state functional magnetic resonance imaging (rs-fMRI) have been widely applied to the analysis and diagnosis of brain diseases, such as Alzheimer's disease and its prodrome, namely mild cognitive impairment (MCI). Constructing a meaningful brain network based on, for example, sparse representation (SR) is the most essential step prior to the subsequent analysis or disease identification. However, the independent coding process of SR fails to capture the intrinsic locality and similarity characteristics in the data. To address this problem, we propose a novel weighted graph (Laplacian) regularized SR framework, based on which BFN can be optimized by considering both intrinsic correlation similarity and local manifold structure in the data, as well as sparsity prior of the brain connectivity. Additionally, the non-convergence of the graph Laplacian in the self-representation model has been solved properly. Combined with a pipeline of sparse feature selection and classification, the effectiveness of our proposed method is demonstrated by identifying MCI based on the constructed BFNs.

Learning Shared and Cluster-Specific Dictionaries for Single Image Super-Resolution

Recently, many multi-dictionary-based sparse representation methods have been proposed for single-image super-resolution (SISR) by learning a sub-dictionary for each specific type of visual content (i.e., a cluster). Although promising reconstruction results have been achieved for certain scenarios, due to the similarity shared among different types of visual content, each sub-dictionary is not learned as discriminatively as expected, which could compromise the visual quality of reconstructed high-resolution (HR) images. In this paper, we propose a novel shared and cluster-specific dictionaries learning method for SISR, where cluster-specific dictionaries can be learned as separate as possible and a dictionary shared among clusters is learned explicitly to explore similarity among clusters. First, low-resolution (LR) and HR image patches extracted from training images are jointly grouped into visual clusters. Then, a shared sub-dictionary and a set of cluster-specific sub-dictionaries are learned simultaneously under the sparse representation framework. In addition, the group sparsity constraint, the locality constraint, and the incoherence penalty term are incorporated into a unified framework to preserve the relationship and structure among the training data in dictionary learning. Finally, an anchored neighborhood regression method is devised to pre-calculate a projection matrix of each learned dictionary atom from LR to its HR space so that an HR image can be more efficiently recovered in the reconstruction stage. Comprehensive experimental results on two widely used benchmark datasets demonstrate the effectiveness and robustness of our method against a number of state-of-the-art methods. The reconstruction results of real-world maritime surveillance images further indicate that the proposed method is well suitable for practical applications.

A Block Alternating Optimization Method for Direction-of-Arrival Estimation With Nested Array

In this paper, direction-of-arrival estimation using nested array is studied in the framework of sparse signal representation. With the vectorization operator, a new real-valued non-negative sparse signal recovery model, which has a wider virtual array aperture, is built. To leverage celebrated compressive sensing algorithms, the continuous parameter space has to be discretized to a number of fixed grid points, which inevitably incurs modeling error caused by off-grid gap. To remedy this issue, a block alternating optimization method is put forth that jointly estimates the sparse signal and refines the locations of grid points. Specifically, inspired by the majorization minimization, the proposed method iteratively minimizes a surrogate function majorizing the given objective function, where only a single block of variables are updated per iteration while the remaining ones are kept fixed. The proposed method features affordable computational complexity, and numerical tests corroborate its superior performance relative to existing alternatives in both overdetermined and underdetermined scenarios.

Interpolation and denoising of seismic signals using orthogonal matching pursuit algorithm: An aplication in VSP and refraction data

An implementation of the Orthogonal Matching Pursuit (OMP) algorithm was used and the results obtained therefrom are presented for simultaneous interpolation and denoising from seismic signals in the framework of sparse signal representation. OMP is an algorithm for sparse signal representation based on orthogonal projections underlying the signal over an over-complete dictionary. This over-complete dictionary was designed using K-times Singular Values Decomposition (K-SVD). In each iteration, OMP calculates a new signal approximation and the approximation error is used in the next iteration to determine the new element. The new element corresponds to the largest magnitude of the inner products between the current residual and the original elements in the dictionary. The implemented algorithm was applied to VSP seismic data and refraction seismic data; results for the application in restored missing traces and denoise signals are presented.

SAR Target Configuration Recognition via Discriminative Statistical Dictionary Learning

The establishment of the dictionary is of crucial importance to sparse representation (SR) based algorithms. It has been proved that learned dictionaries are more compact and have better performance than predefined ones. A dictionary learning (DL) algorithm is proposed for synthetic aperture radar (SAR) target configuration recognition in a statistical way with discriminative power embedded in under the SR framework, which is named as discriminative statistical DL (DSDL) in this paper. A better description of the SAR image is obtained from the statistical standpoint and, thus, improving the robustness of the proposed algorithm. To make the learned dictionary more discriminative, the dictionary is finally determined while minimizing differences within the same target configuration and, meanwhile, maximizing differences among different configurations. The proposed DSDL algorithm can provide dictionaries for SR-based recognition algorithms. Experimental results on the moving and stationary target acquisition and recognition database validate the effectiveness and robustness of the proposed DSDL-SR recognition algorithm. A comparison with other recognition techniques further demonstrates its superiority.

Multistage Pooling for Blind Quality Prediction of Asymmetric Multiply-Distorted Stereoscopic Images

Quality prediction for asymmetric multiply-distorted stereoscopic images (MDSIs) confronts more challenges than previous stereoscopic image quality assessment (SIQA) issues, whereas the existing no-reference SIQA methods have been limited to understand the asymmetric distortions and multiple distortions simultaneously for general-purpose blind quality prediction. In this paper, we propose a multistage pooling (MUSP) model for quality prediction of asymmetric MDSIs. In the training stage, we establish multimodal sparse representation framework for phase and amplitude components, respectively. In the testing stage, we use an MUSP strategy to simulate the pooling procedure undergoing multimodal quality pooling, feature pooling, binocular pooling, and phase-amplitude quality pooling in order. Experimental results on our new established database (NBU-MDSID Phase-II) demonstrate the effectiveness of our blind metric.