Sparse Representation Model Research Articles

Multi-Feature Weighted Sparse Graph for SAR Image Analysis

Sparse representation (SR) method has the advantages of good category distinguishing performance, noise robustness, and data adaptiveness. In this article, a multi-feature weighted sparse graph (MWSG) is presented for synthetic aperture radar (SAR) image analysis. First, multiple types of features are extracted to fully describe the characteristics of SAR image. Then, multiple SRs of samples in multiple feature spaces are obtained by solving a weighted joint SR model, in which the weight is the Gaussian kernel distance among samples. Moreover, a new fusion mechanism is given to integrate multiple weighted SRs, which aims to eliminate the negative influence of the singular data, so the MWSG is obtained. Afterward, the brief steps of the SAR image segmentation and semisupervised classification based on MWSG are stated. A series of experiments on the simulated and real SAR images shows that the MWSG has better performance than other existing relevant methods.

Multi-Direction Dictionary Learning Based Depth Map Super-Resolution With Autoregressive Modeling

3D depth cameras have become more and more popular in recent years. However, depth maps captured by these cameras can hardly be used in 3D reconstruction directly because they often suffer from low resolution and blurring depth discontinuities. Super resolution of depth maps is necessary. In depth maps, the edge areas play more important role and demonstrate distinct geometry directions compared with natural images. However, most existing super-resolution methods ignore this fact, and they can not handle depth edges properly. Motivated by this, we propose a compound method that combines multi-direction dictionary sparse representation and autoregressive (AR) models, so that the depth edges are presented precisely at different levels. In the patch level, the depth edge patches with geometry directions are well represented by the pre-trained multi-directional dictionaries. Compared with a universal dictionary, multiple dictionaries trained from different directional patches can represent the directional depth patch much better. In the finer pixel level, we utilize an adaptive AR model to represent the local correlation patterns in small areas. Extensive experimental results on both synthetic and real datasets demonstrate that, the proposed model outperforms state-of-the-art depth map super-resolution methods in terms of both quantitative metrics and subjective visual quality.

Adversarial Noise Attacks of Deep Learning Architectures: Stability Analysis via Sparse-Modeled Signals

Despite their impressive performance, deep convolutional neural networks (CNN) have been shown to be sensitive to small adversarial perturbations. These nuisances, which one can barely notice, are powerful enough to fool sophisticated and well performing classifiers, leading to ridiculous misclassification results. In this paper, we analyze the stability of state-of-the-art deep learning classification machines to adversarial perturbations, where we assume that the signals belong to the (possibly multilayer) sparse representation model. We start with convolutional sparsity and then proceed to its multilayered version, which is tightly connected to CNN. Our analysis links between the stability of the classification to noise and the underlying structure of the signal, quantified by the sparsity of its representation under a fixed dictionary. In addition, we offer similar stability theorems for two practical pursuit algorithms, which are posed as two different deep learning architectures—the layered thresholding and the layered basis pursuit. Our analysis establishes the better robustness of the later to adversarial attacks. We corroborate these theoretical results by numerical experiments on three datasets: MNIST, CIFAR-10 and CIFAR-100.

Convolutional Sparse Representation of Injected Details for Pansharpening

In this letter, we address the pansharpening problem, which focuses on constructing a high-resolution (HR) multispectral (MS) image from a low-resolution (LR) MS and an HR panchromatic (Pan) image. The accuracy of pansharpening method based on sparse representation (SR) mainly depends on the construction of dictionary and the learning of sparse coefficients, while the details injection (DI)-based pansharpening method sharpens the MS bands by adding the proper spatial details from Pan. The combination of SR and DI has been put forward as the pansharpening method based on SR of injected details (SR-D). However, limited to the patch-based manner, pansharpening with traditional SR model faces two disadvantages, i.e., limited ability in detail preservation and high sensitivity to misregistration. In this letter, we replace the traditional SR model with convolutional SR (CSR) as a global SR model in the SR-D method and propose a new pansharpening method called CSR of injected details (CSR-D) to overcome the above-mentioned two drawbacks. Experimental results on the IKONOS and WorldView2 data sets show that the proposed method can achieve remarkable spectral and spatial quality on both reduced scale and full scale.

Layer-Wise Pre-Training Low-Rank NMF Model for Mammogram-Based Breast Tumor Classification

Image-based breast tumor classification is an active and challenging problem. In this paper, a robust breast tumor classification framework is presented based on deep feature representation learning and exploiting available information in existing samples. Feature representation learning of mammograms is fulfilled by a modified nonnegative matrix factorization model called LPML-LRNMF, which is motivated by hierarchical learning and layer-wise pre-training (LP) strategy in deep learning. Low-rank (LR) constraint is integrated into the feature representation learning model by considering the intrinsic characteristics of mammograms. Moreover, the proposed LPML-LRNMF model is optimized via alternating direction method of multipliers and the corresponding convergence is analyzed. For completing classification, an inverse projection sparse representation model is introduced to exploit information embedded in existing samples, especially in test ones. Experiments on the public dataset and actual clinical dataset show that the classification accuracy, specificity and sensitivity achieve the clinical acceptance level.

Robust visual tracking using discriminative sparse collaborative map

Visual tracking is a challenging task as it needs to consider the appearance variations due to some intrinsic and extrinsic interference factors in the process of tracking. This paper proposes a robust visual tracking algorithm based on the discriminative sparse collaborative (DSC) map and the alternating direction method of multipliers (ADMM). In the proposed visual tracker, named DSC tracker, a novel multi-task reverse sparse representation model based on the group sparse representation and group collaborative representation is proposed. Different from the traditional trackers that use the accelerated proximal gradient for solution, an effective method called ADMM is adopted to solve the proposed optimization model. With the solution, we can construct the discriminative features that contain the sparsity and coordination for the candidates on all templates simultaneously. Many comparison experiments illustrate that the proposed DSC tracker outperforms the DSS tracker as well as several state-of-the-art trackers.

Sparsity-assisted bearing fault diagnosis using multiscale period group lasso

Fault diagnosis methods based on sparse representation (SR) theory have achieved great success recently. However, it is still challenging to extract features from signals with strong noise interference. In this paper, a new method named multiscale period group Lasso (MPG Lasso) is proposed, which is a multiscale SR model performed in different wavelet subbands and uses nonconvex regularization functions to enhance sparsity within and across groups. The improvements of this method over conventional SR models are mainly made in the three aspects. First, impulses are extracted in the wavelet domain which is likely to produce more sparse results. Second, a multiscale periodic prior is embedded within the penalty function to make the extraction of characteristic frequency more accurate. Third, a rule of adaptive hyper-parameter setting in the model is further studied to simplify the industrial application of MPG Lasso. Performance of MPG Lasso is verified by a series of simulation experiments and diagnosis of fault bearings. The results show that MPG Lasso gets better performance than other up-to-date methods.

Collaborative Sparse Coding with Smoothness Regularization for Hyperspectral-Image Classification

Hyperspectral-image (HSI) classification plays a key role in numerous applications in remote sensing, urban planning, and environmental monitoring. Sparse-representation models have been increasingly explored for HSI classification because of their compactness, flexibility, and discriminative power. In this article, a novel HSI scheme is proposed based on collaborative sparse coding combined with smoothness regularization (CSCSR). First, based on the spatial piecewise continuity of HSIs, spectral-spatial preprocessing is performed to improve classification accuracy. Second, a collaborative sparse-coding model with smoothness regularization is proposed and applied for HSI classification. In our model, the sparsity level and smoothness regularization are tuned to improve classification performance. In addition, weighted pixel similarities are computed in pixel neighborhoods and then used to incorporate spatial information in the HSI classification scheme. A feature-sign search algorithm is used for sparse coding of feature descriptors. Experimental results on real HSI data sets demonstrate that the proposed CSCSR method effectively outperforms the current state-of-the-art HSI classifiers in terms of both qualitative and quantitative metrics.

Image Fusion Using Adjustable Non-subsampled Shearlet Transform

Multiscale transform (MST) and sparse representation (SR)-based image fusion techniques are widely used in many applications. However, the existing fusion methods are inefficient to perfectly seize significant details and texture information of input images because of some limitations of MST-and SR-based techniques. Moreover, it is quite important to measure singularities and structural information of the fused image to objectively measure the performance of different fusion techniques. Therefore, a metric which can efficiently measure singularity and structural information of the fused image would be quite useful for comparison of different fusion techniques. To address these issues, a modified Meyer window-based adjustable nonsubsampled shearlet transform (ANSST) is proposed for decomposition of preregistered input images into low-and high-frequency coefficients. The low-frequency bands are fused by convolutional SR modeling. The high-frequency bands are fused by our proposed information entropy, standard deviation, and range descriptor, which considers entropy, standard deviation, and range-filtering features. Moreover, a metric $Q_{SS}$ is formulated to measure the singularities and structural information of the fused image. The $Q_{SS}$ metric is developed by using the concept of the proposed native division and native difference filtering. To show the applicability of the proposed image framework, the proposed ANSST is applied for image denoising. Experimental results verify the effectiveness of the proposed fusion method and the metric $Q_{SS}$ .

Image fusion method based on spatially masked convolutional sparse representation

The technique of sparse representation (SR) has achieved enormous successes in multi-source image fusion. However, using SR-based fusion methods, there exists the performance degradation in limited detail preservation caused by the independent processing of image patches. To remedy this deficiency, in this paper, a novel method based on spatially masked convolutional sparse representation (SMCSR-based) is proposed for image fusion, which is composed of three steps as follows. Firstly, low-frequency and high-frequency bands are separated from each source image by the designed two-scale gradient optimization approach. Secondly, the SMCSR model is employed to fuse the high-frequency bands, and the “average" rule is applied to the combination of the low-frequency bands. At last, the fused image is reconstructed. Compared with traditional SR-based algorithms, the proposed SMCSR-based method is focused on entire images instead of those divided patches to reduce detail-loss. In addition, this method can overcome the difficulty in the selection of decomposition levels originated by multi-scale transform (MST) based fusion strategies, as well as also suppress the boundary artifacts produced by the traditional convolutional sparse representation (CSR) model. Extensive experiments and related analysis are given to verify the effectiveness of the proposed SMCSR-based fusion method.

Ultrasonic image processing based on fusion super-resolution reconstruction of familiar models

Ultrasound image technology is to measure the energy and time of arrival of the reflected echo after the pulse acoustic signal is sent out by the ultrasonic wave. Usually, the distance between the ultrasonic source and the reflector is measured. Super-resolution image reconstruction aims to recover high-resolution images from one or more low-resolution images. Super-resolution image reconstruction is a software approach to solve the problem of low-resolution images by overcoming the limitations of hardware. In this paper, an image super-resolution reconstruction method based on sparse representation model and multi-feature fusion is proposed. Sparse dictionary is used to learn and reconstruct the luminance details of ultrasonic images, and edge interpolation is used to improve the edge clarity. Experimental results show that the proposed method is superior to Bicubic interpolation, SCSR and JOR in PSNR, and is 0.35 dB higher than RAISR. On the FSIM index, this method is also slightly better than other comparison methods, which can get better reconstruction results. Visual effects and numerical evaluation results of reconstructed images are better than several comparison methods.

Mask Sparse Representation Based on Semantic Features for Thermal Infrared Target Tracking

Thermal infrared (TIR) target tracking is a challenging task as it entails learning an effective model to identify the target in the situation of poor target visibility and clutter background. The sparse representation, as a typical appearance modeling approach, has been successfully exploited in the TIR target tracking. However, the discriminative information of the target and its surrounding background is usually neglected in the sparse coding process. To address this issue, we propose a mask sparse representation (MaskSR) model, which combines sparse coding together with high-level semantic features for TIR target tracking. We first obtain the pixel-wise labeling results of the target and its surrounding background in the last frame, and then use such results to train target-specific deep networks using a supervised manner. According to the output features of the deep networks, the high-level pixel-wise discriminative map of the target area is obtained. We introduce the binarized discriminative map as a mask template to the sparse representation and develop a novel algorithm to collaboratively represent the reliable target part and unreliable target part partitioned with the mask template, which explicitly indicates different discriminant capabilities by label 1 and 0. The proposed MaskSR model controls the superiority of the reliable target part in the reconstruction process via a weighted scheme. We solve this multi-parameter constrained problem by a customized alternating direction method of multipliers (ADMM) method. This model is applied to achieve TIR target tracking in the particle filter framework. To improve the sampling effectiveness and decrease the computation cost at the same time, a discriminative particle selection strategy based on kernelized correlation filter is proposed to replace the previous random sampling for searching useful candidates. Our proposed tracking method was tested on the VOT-TIR2016 benchmark. The experiment results show that the proposed method has a significant superiority compared with various state-of-the-art methods in TIR target tracking.

BSBL-Based DOA and Polarization Estimation with Linear Spatially Separated Polarization Sensitive Array

The problem of multiple incident signals’ direction of arrival (DOA) and polarization estimation with linear spatially separated polarization sensitive array (SS-PSA) is investigated in sparse Bayesian learning (SBL) framework. SS-PSA is widely studied due to its low mutual coupling compared with the spatially collocated polarization sensitive array. On the one hand, the sparse representation of data model of proposed array can be expressed skillfully as a block-sparse representation. On the other hand, block sparse Bayesian learning (BSBL) algorithm has excellent performance in recovering the block-sparse signals. Therefore, in this paper, BSBL algorithm is extended to SS-PSA for DOA and polarization estimation. Firstly, a sparse representation model without parameters coupling is established, where the sparse coefficient vector is a block-sparse signal. Secondly, the expectation–maximization method in BSBL framework, i.e., BSBL-EM algorithm, is proposed to recover the block-sparse signal. Lastly, angles estimation can be obtained from the recovered sparse signal according to the intra-block correlation. Simulation results demonstrate that the BSBL-EM algorithm used in DOA and polarization estimation with SS-PSA exhibits better performance compared with Block Orthogonal Matching Pursuit algorithm and Group Basis Pursuit.

Joint Sparse Learning With Nonlocal and Local Image Priors for Image Error Concealment

Joint sparse representation (JSR) model has recently emerged as a powerful technique with wide variety of applications. In this paper, the JSR model is extended to error concealment (EC) application, being effective to recover the original image from its corrupted version. This model is based on jointly learning a dictionary pair and two mapping matrices that are trained offline from external training images. Given the trained dictionaries and mappings, the restoration is done by transferring the recovery problem into the sparse representation domain with respect to the trained dictionaries, which is further transformed into a common space using the respective mapping matrices. Then, the reconstructed image is obtained by back projection into the spatial domain. In order to improve the accuracy and stability of the proposed JSR-based EC algorithm and avoid unexpected artifacts, the local and non-local priors are seamlessly integrated into the JSR model. The non-local prior is based on the self-similarity within natural images and helps to find an accurate sparse representation by taking a weighted average of similar areas throughout the image. The local prior is based on learning the local structural regularity of the natural images and helps to regularize the sparse representation, exploiting the strong correlation in the small local areas within the image. Compared with the state-of-the-art EC algorithms, the results show that the proposed method has better reconstruction performance in terms of objective and subjective evaluations.

Power-Constrained Image Contrast Enhancement Through Sparse Representation by Joint Mixed-Norm Regularization

Power-constrained image contrast enhancement is a fundamental step for improving the battery life of modern consumer devices with embedded emissive-display panels, such as organic light-emitting diodes (OLEDs). The conventional power-constrained image contrast enhancement in OLED displays is typically performed using histogram-relevant priors or heuristic curve-fitted techniques. This results in underexposure effects or color-tone changes in the reconstructed image. Therefore, this paper proposes a novel power-constrained sparse representation model by joint l2, 1, γ, and isotropic total variation norm (called mixed-norm) regularized sparse coding to simultaneously improve power saving and the perceptible visual quality of the OLED displays. The qualitative and quantitative experiments demonstrate that the proposed technique noticeably outperforms the state-of-the-art power-constrained contrastenhancement techniques.

A 2D Nested Array Based DOA Estimator for Incoherently Distributed Sources via Sparse Representation Utilizing L1-Norm

Nested arrays are sparse arrays composed of subarrays with nonuniform sensor spacing. Compared with traditional uniform arrays, nested arrays have more degree of freedoms (DOFs) and larger apertures. In this paper, a nested array has been proposed as well as a direction-of-arrival (DOA) estimation method for two-dimensional (2D) incoherently distributed (ID) sources. A virtual array is firstly obtained through vectorization of the cross-correlation matrix of subarrays. Sensor positions of the virtual array and the optimal configuration of the nested array are derived next. Then rotational invariance relationship for generalized steering matrix of the virtual array with respect to nominal azimuth is deduced. According to the rotational invariance relationship, sparse representation model under l1-norm constraint is established, which is resolved by transferring the objective function to second-order cone constraints and combining a estimation residual error constraint for receive vector of the virtual array. Simulations are conducted to investigate the effectiveness of the proposed method in underdetermined situation and examine different experiment factors including SNR, snapshots, and angular spreads as well as sensor number of subarrays. Results show that the proposed method has better performance than uniform parallel arrays with the same number of sensors.

Traveling distance estimation for dispersive Lamb waves through sparse Bayesian learning strategy

Lamb wave is a promising tool for the nondestructive testing and structural health monitoring (SHM) of plate-like structures. The dispersive effect is an intrinsic property of guided waves, making the energy of the incoming wave packets spreading out in time domain so that wave packets are easily overlapped, which causes the traveling distances of the wave packets hard to be estimated and thus degrades the resolution of imaging. Traveling distance estimation is the basis of damage localization in Lamb wave based SHM. To deal with these problems, a sparse Bayesian learning (SBL) strategy based method is proposed to sparsely estimate the traveling distance of each dispersive wave packet. To establish a spare representation model, an overcomplete dictionary with each atom corresponding to a dispersive Lamb wave is designed to decompose the measured dispersive signal in frequency domain. The sparse representation model is based on a prior knowledge that the number of wave packets in the measured signal is sparse comparing with the number of atoms of the designed dictionary. Then the distance spectrum, the amplitude coefficients in distance domain, can be sparsely recovered via the SBL strategy. Dispersion compensated signal can also be achieved using the distance spectrum and another designed non-dispersive dictionary. Results from simulations and experiments on a plate both demonstrate the effectiveness of the proposed method.

A novel sparse representation model for pedestrian abnormal trajectory understanding

Pedestrian abnormal trajectory understanding based on video surveillance systems can improve public safety. However, manually identifying pedestrian abnormal trajectories is usually a prohibitive workload. The objective of this study is to propose an automatic method for understanding pedestrian abnormal trajectories. An improved sparse representation model, namely information entropy constrained trajectory representation method (IECTR), is developed for pedestrian trajectory classification. It aims to reduce the entropy for trajectory representation and to obtain superior analyzing results. In the proposed method, the orthogonal matching pursuit (OMP) is embedded in the expectation maximization (EM) method to iteratively obtain the selection probabilities and the sparse coefficients. In addition, the lower-bound sparser condition of Lp-minimization (0 < p < 1) is applied in the proposed method to guarantee salient solutions. In order to validate the performance and effectiveness of the proposed method, classification experiments are conducted using five pedestrian trajectory datasets. The results show that the identification accuracy of the proposed method is superior to the compared methods, including naïve Bayes classifier (NBC), support vector machine (SVM), k-nearest neighbor (kNN), and typical sparse representation-based methods.

Identification of fungi-contaminated peanuts using hyperspectral imaging technology and joint sparse representation model.

Peanuts with fungal contamination may contain aflatoxin, a highly carcinogenic substance. We propose the use of hyperspectral imaging to quickly and noninvasively identify fungi-contaminated peanuts. The spectral data and spatial information of hyperspectral images were exploited to improve identification accuracy. In addition, successive projection was adopted to select the bands sensitive to fungal contamination. Furthermore, the joint sparse representation based classification (JSRC), which considers neighboring pixels as belonging to the same class, was adopted, and the support vector machine (SVM) classifier was used for comparison. Experimental results show that JSRC outperforms SVM regarding robustness against random noise and considering pixels at the edge of the peanut kernel. The classification accuracy of JSRC reached 99.2% and 98.8% at pixel scale, at least 98.4% and 96.8% at kernel scale for two peanut varieties, retrieving more accurate and consistent results than SVM. Moreover, fungi-contaminated peanuts were correctly marked in both learning and test images.

Adaptive lq-norm constrained general nonlocal self-similarity regularizer based sparse representation for single image super-resolution

Sparse representation (SR) with the traditional nonlocal self-similarity (NLSS) regularizer has a brilliant future in handling single image super-resolution (SISR) inverse problem. However, such NLSS regularizers proposed so far always favor the fixed lq-norm constraint, making it difficult to cater the statistical diversity of the image content. As a result, the reconstruction capability of SR model is adversely influenced. To cope with the drawback, we first devise an adaptive lq-norm constrained general NLSS regularizer, which can integrate the advantages of the traditional NLSS prior and the row NLSS prior and adaptively assign different q values to handle the different image contents, and then incorporate it into SR model. Moreover, previous works only consider the additive white Gaussian noise case and neglect to research the impulse noise case in SR based SISR framework. For this purpose, our work will further consider these factors. Finally, both the iteratively reweighted least squares and the standard iterative shrinkage algorithms are adopted for solving our SR model. Experiments reveal that the reconstruction capability of our method is better than many outstanding SISR reconstruction methods.