THE SPARSE REPRESENTATION RELATED WITH FRACTIONAL HEAT EQUATIONS

This study introduces a pre-orthogonal adaptive Fourier decomposition(POAFD)to obtain approximations and numerical solutions to the fractional Laplacian initial value problem and the extension problem of Caffarelli and Silvestre(generalized Poisson equation).As a first step,the method expands the initial data function into a sparse series of the fundamental solutions with fast convergence,and,as a second step,makes use of the semigroup or the reproducing kernel property of each of the expanding entries.Experiments show the effectiveness and efficiency of the proposed series solutions.

A weighted block cooperative sparse representation algorithm based on visual saliency dictionary

Unconstrained face images are interfered by many factors such as illumination,posture,expression,occlusion,age,accessories and so on,resulting in the randomness of the noise pollution implied in the original samples.In order to improve the sample quality,a weighted block cooperative sparse representation algorithm is proposed based on visual saliency dictionary.First,the algorithm uses the biological visual attention mechanism to quickly and accurately obtain the face salient target and constructs the visual salient dictionary.Then,a block cooperation framework is presented to perform sparse coding for different local structures of human face,and the weighted regular term is introduced in the sparse representation process to enhance the identification of information hidden in the coding coefficients.Finally,by synthesising the sparse representation results of all visual salient block dictionaries,the global coding residual is obtained and the class label is given.The experimental results on four databases,that is,AR,extended Yale B,LFW and PubFig,indicate that the combination of visual saliency dictionary,block cooperative sparse representation and weighted constraint coding can effectively enhance the accuracy of sparse representation of the samples to be tested and improve the performance of unconstrained face recognition.

Multi-Layer Deep Sparse Representation for Biological Slice Image Inpainting

Biological slices are an effective tool for studying the physiological structure and evolutionmechanism of biological systems.However,due to the complexity of preparation technology and the presence of many uncontrollable factors during the preparation processing,leads to problems such as difficulty in preparing slice images and breakage of slice images.Therefore,we proposed a biological slice image small-scale corruption inpainting algorithm with interpretability based on multi-layer deep sparse representation,achieving the high-fidelity reconstruction of slice images.We further discussed the relationship between deep convolutional neural networks and sparse representation,ensuring the high-fidelity characteristic of the algorithm first.A novel deep wavelet dictionary is proposed that can better obtain image prior and possess learnable feature.And multi-layer deep sparse representation is used to implement dictionary learning,acquiring better signal expression.Compared with methods such as NLABH,Shearlet,Partial Differential Equation(PDE),K-Singular Value Decomposition(K-SVD),Convolutional Sparse Coding,and Deep Image Prior,the proposed algorithm has better subjective reconstruction and objective evaluation with small-scale image data,which realized high-fidelity inpainting,under the condition of small-scale image data.And theOn2-level time complexitymakes the proposed algorithm practical.The proposed algorithm can be effectively extended to other cross-sectional image inpainting problems,such as magnetic resonance images,and computed tomography images.

Super-Resolution Based on Curvelet Transform and Sparse Representation

Super-resolution techniques are used to reconstruct an image with a high resolution from one or more low-resolution image(s).In this paper,we proposed a single image super-resolution algorithm.It uses the nonlocal mean filter as a prior step to produce a denoised image.The proposed algorithm is based on curvelet transform.It converts the denoised image into low and high frequencies(sub-bands).Then we applied a multi-dimensional interpolation called Lancozos interpolation over both sub-bands.In parallel,we applied sparse representation with over complete dictionary for the denoised image.The proposed algorithm then combines the dictionary learning in the sparse representation and the interpolated sub-bands using inverse curvelet transform to have an image with a higher resolution.The experimental results of the proposed super-resolution algorithm show superior performance and obviously better-recovering images with enhanced edges.The comparison study shows that the proposed super-resolution algorithm outperforms the state-of-the-art.The mean absolute error is 0.021±0.008 and the structural similarity index measure is 0.89±0.08.

Image Fusion Based on NSCT and Sparse Representation for Remote Sensing Data

The practice of integrating images from two or more sensors collected from the same area or object is known as image fusion.The goal is to extract more spatial and spectral information from the resulting fused image than from the component images.The images must be fused to improve the spatial and spectral quality of both panchromatic and multispectral images.This study provides a novel picture fusion technique that employs L0 smoothening Filter,Non-subsampled Contour let Transform(NSCT)and Sparse Representation(SR)followed by the Max absolute rule(MAR).The fusion approach is as follows:first,the multispectral and panchromatic images are divided into lower and higher frequency components using the L0 smoothing filter.Then comes the fusion process,which uses an approach that combines NSCT and SR to fuse low frequency components.Similarly,the Max-absolute fusion rule is used to merge high frequency components.Finally,the final image is obtained through the disintegration of fused low and high frequency data.In terms of correlation coefficient,Entropy,spatial frequency,and fusion mutual information,our method outperforms other methods in terms of image quality enhancement and visual evaluation.

Non Sub-Sampled Contourlet with Joint Sparse Representation Based Medical Image Fusion

Medical Image Fusion is the synthesizing technology for fusing multi-modal medical information using mathematical procedures to generate better visual on the image content and high-quality image output.Medical image fusion represents an indispensible role infixing major solutions for the complicated medical predicaments,while the recent research results have an enhanced affinity towards the preservation of medical image details,leaving color distortion and halo artifacts to remain unaddressed.This paper proposes a novel method of fusing Computer Tomography(CT)and Magnetic Resonance Imaging(MRI)using a hybrid model of Non Sub-sampled Contourlet Transform(NSCT)and Joint Sparse Representation(JSR).This model gratifies the need for precise integration of medical images of different modalities,which is an essential requirement in the diagnosing process towards clinical activities and treating the patients accordingly.In the proposed model,the medical image is decomposed using NSCT which is an efficient shift variant decomposition transformation method.JSR is exercised to extricate the common features of the medical image for the fusion process.The performance analysis of the proposed system proves that the proposed image fusion technique for medical image fusion is more efficient,provides better results,and a high level of distinctness by integrating the advantages of complementary images.The comparative analysis proves that the proposed technique exhibits better-quality than the existing medical image fusion practices.

DOA Estimation Based on Sparse Representation of the Fractional Lower Order Statistics in Impulsive Noise

This paper is mainly to deal with the problem of direction of arrival(DOA) estimations of multiple narrow-band sources impinging on a uniform linear array under impulsive noise environments. By modeling the impulsive noise as α-stable distribution, new methods which combine the sparse signal representation technique and fractional lower order statistics theory are proposed. In the new algorithms, the fractional lower order statistics vectors of the array output signal are sparsely represented on an overcomplete basis and the DOAs can be effectively estimated by searching the sparsest coefficients. To enhance the robustness performance of the proposed algorithms,the improved algorithms are advanced by eliminating the fractional lower order statistics of the noise from the fractional lower order statistics vector of the array output through a linear transformation. Simulation results have shown the effectiveness of the proposed methods for a wide range of highly impulsive environments.

Multi-task Joint Sparse Representation Classification Based on Fisher Discrimination Dictionary Learning

Recently,sparse representation classification(SRC)and fisher discrimination dictionary learning(FDDL)methods have emerged as important methods for vehicle classification.In this paper,inspired by recent breakthroughs of discrimination dictionary learning approach and multi-task joint covariate selection,we focus on the problem of vehicle classification in real-world applications by formulating it as a multi-task joint sparse representation model based on fisher discrimination dictionary learning to merge the strength of multiple features among multiple sensors.To improve the classification accuracy in complex scenes,we develop a new method,called multi-task joint sparse representation classification based on fisher discrimination dictionary learning,for vehicle classification.In our proposed method,the acoustic and seismic sensor data sets are captured to measure the same physical event simultaneously by multiple heterogeneous sensors and the multi-dimensional frequency spectrum features of sensors data are extracted using Mel frequency cepstral coefficients(MFCC).Moreover,we extend our model to handle sparse environmental noise.We experimentally demonstrate the benefits of joint information fusion based on fisher discrimination dictionary learning from different sensors in vehicle classification tasks.

Local Robust Sparse Representation for Face Recognition With Single Sample per Person

The purpose of this paper is to solve the problem of robust face recognition(FR) with single sample per person(SSPP). In the scenario of FR with SSPP, we present a novel model local robust sparse representation(LRSR) to tackle the problem of query images with various intra-class variations,e.g., expressions, illuminations, and occlusion. FR with SSPP is a very difficult challenge due to lacking of information to predict the possible intra-class variation of the query images.The key idea of the proposed method is to combine a local sparse representation model and a patch-based generic variation dictionary learning model to predict the possible facial intraclass variation of the query images. The experimental results on the AR database, Extended Yale B database, CMU-PIE database and LFW database show that the proposed method is robust to intra-class variations in FR with SSPP, and outperforms the state-of-art approaches.

Particle Filter Object Tracking Algorithm Based on Sparse Representation and Nonlinear Resampling

Object tracking with abrupt motion is an important research topic and has attracted wide attention.To obtain accurate tracking results,an improved particle filter tracking algorithm based on sparse representation and nonlinear resampling is proposed in this paper. First,the sparse representation is used to compute particle weights by considering the fact that the weights are sparse when the object moves abruptly,so the potential object region can be predicted more precisely. Then,a nonlinear resampling process is proposed by utilizing the nonlinear sorting strategy,which can solve the problem of particle diversity impoverishment caused by traditional resampling methods. Experimental results based on videos containing objects with various abrupt motions have demonstrated the effectiveness of the proposed algorithm.

Intelligent Fusion of Infrared and Visible Image Data Based on Convolutional Sparse Representation and Improved Pulse-Coupled Neural Network

Multi-source information can be obtained through the fusion of infrared images and visible light images,which have the characteristics of complementary information.However,the existing acquisition methods of fusion images have disadvantages such as blurred edges,low contrast,and loss of details.Based on convolution sparse representation and improved pulse-coupled neural network this paper proposes an image fusion algorithm that decompose the source images into high-frequency and low-frequency subbands by non-subsampled Shearlet Transform(NSST).Furthermore,the low-frequency subbands were fused by convolutional sparse representation(CSR),and the high-frequency subbands were fused by an improved pulse coupled neural network(IPCNN)algorithm,which can effectively solve the problem of difficulty in setting parameters of the traditional PCNN algorithm,improving the performance of sparse representation with details injection.The result reveals that the proposed method in this paper has more advantages than the existing mainstream fusion algorithms in terms of visual effects and objective indicators.

Unsupervised seismic facies analysis using sparse representation spectral clustering

Traditional unsupervised seismic facies analysis techniques need to assume that seismic data obey mixed Gaussian distribution.However,fi eld seismic data may not meet this condition,thereby leading to wrong classifi cation in the application of this technology.This paper introduces a spectral clustering technique for unsupervised seismic facies analysis.This algorithm is based on on the idea of a graph to cluster the data.Its kem is that seismic data are regarded as points in space,points can be connected with the edge and construct to graphs.When the graphs are divided,the weights of the edges between the different subgraphs are as low as possible,whereas the weights of the inner edges of the subgraph should be as high as possible.That has high computational complexity and entails large memory consumption for spectral clustering algorithm.To solve the problem this paper introduces the idea of sparse representation into spectral clustering.Through the selection of a small number of local sparse representation points,the spectral clustering matrix of all sample points is approximately represented to reduce the cost of spectral clustering operation.Verifi cation of physical model and fi eld data shows that the proposed approach can obtain more accurate seismic facies classification results without considering the data meet any hypothesis.The computing efficiency of this new method is better than that of the conventional spectral clustering method,thereby meeting the application needs of fi eld seismic data.

Low-Rank and Sparse Representation with Adaptive Neighborhood Regularization for Hyperspectral Image Classification

Low-Rank and Sparse Representation(LRSR)method has gained popularity in Hyperspectral Image(HSI)processing.However,existing LRSR models rarely exploited spectral-spatial classification of HSI.In this paper,we proposed a novel Low-Rank and Sparse Representation with Adaptive Neighborhood Regularization(LRSR-ANR)method for HSI classification.In the proposed method,we first represent the hyperspectral data via LRSR since it combines both sparsity and low-rankness to maintain global and local data structures simultaneously.The LRSR is optimized by using a mixed Gauss-Seidel and Jacobian Alternating Direction Method of Multipliers(M-ADMM),which converges faster than ADMM.Then to incorporate the spatial information,an ANR scheme is designed by combining Euclidean and Cosine distance metrics to reduce the mixed pixels within a neighborhood.Lastly,the predicted labels are determined by jointly considering the homogeneous pixels in the classification rule of the minimum reconstruction error.Experimental results based on three popular hyperspectral images demonstrate that the proposed method outperforms other related methods in terms of classification accuracy and generalization performance.

Fractional-order Sparse Representation for Image Denoising

Sparse representation models have been shown promising results for image denoising. However, conventional sparse representation-based models cannot obtain satisfactory estimations for sparse coefficients and the dictionary. To address this weakness, in this paper, we propose a novel fractional-order sparse representation(FSR) model. Specifically, we cluster the image patches into K groups, and calculate the singular values for each clean/noisy patch pair in the wavelet domain. Then the uniform fractional-order parameters are learned for each cluster.Then a novel fractional-order sample space is constructed using adaptive fractional-order parameters in the wavelet domain to obtain more accurate sparse coefficients and dictionary for image denoising. Extensive experimental results show that the proposed model outperforms state-of-the-art sparse representation-based models and the block-matching and 3D filtering algorithm in terms of denoising performance and the computational efficiency.

Pulse Signal Recovery Method Based on Sparse Representation

Pulse signal recovery is to extract useful amplitude and time information from the pulse signal contaminated by noise. It is a great challenge to precisely recover the pulse signal in loud background noise. The conventional approaches,which are mostly based on the distribution of the pulse energy spectrum,do not well determine the locations and shapes of the pulses. In this paper,we propose a time domain method to reconstruct pulse signals. In the proposed approach,a sparse representation model is established to deal with the issue of the pulse signal recovery under noise conditions. The corresponding problem based on the sparse optimization model is solved by a matching pursuit algorithm. Simulations and experiments validate the effectiveness of the proposed approach on pulse signal recovery.

Research on image sentiment analysis technology based on sparse representation

Many methods based on deep learning have achieved amazing results in image sentiment analysis.However,these existing methods usually pursue high accuracy,ignoring the effect on model training efficiency.Considering that when faced with large-scale sentiment analysis tasks,the high accuracy rate often requires long experimental time.In view of the weakness,a method that can greatly improve experimental efficiency with only small fluctuations in model accuracy is proposed,and singular value decomposition(SVD)is used to find the sparse feature of the image,which are sparse vectors with strong discriminativeness and effectively reduce redundant information;The authors propose the Fast Dictionary Learning algorithm(FDL),which can combine neural network with sparse representation.This method is based on K-Singular Value Decomposition,and through iteration,it can effectively reduce the calculation time and greatly improve the training efficiency in the case of small fluctuation of accuracy.Moreover,the effectiveness of the proposed method is evaluated on the FER2013 dataset.By adding singular value decomposition,the accuracy of the test suite increased by 0.53%,and the total experiment time was shortened by 8.2%;Fast Dictionary Learning shortened the total experiment time by 36.3%.

Two-Dimensional Direction Finding via Sequential Sparse Representations

The problem of two-dimensional direction finding is approached by using a multi-layer Lshaped array. The proposed method is based on two sequential sparse representations,fulfilling respectively the estimation of elevation angles,and azimuth angles. For the estimation of elevation angles,the weighted sub-array smoothing technique for perfect data decorrelation is used to produce a covariance vector suitable for exact sparse representation,related only to the elevation angles. The estimates of elevation angles are then obtained by sparse restoration associated with this elevation angle dependent covariance vector. The estimates of elevation angles are further incorporated with weighted sub-array smoothing to yield a second covariance vector for precise sparse representation related to both elevation angles,and azimuth angles. The estimates of azimuth angles,automatically paired with the estimates of elevation angles,are finally obtained by sparse restoration associated with this latter elevation-azimuth angle related covariance vector. Simulation results are included to illustrate the performance of the proposed method.

Modeling of unsupervised knowledge graph of events based on mutual information among neighbor domains and sparse representation

Text event mining,as an indispensable method of text mining processing,has attracted the extensive attention of researchers.A modeling method for knowledge graph of events based on mutual information among neighbor domains and sparse representation is proposed in this paper,i.e.UKGE-MS.Specifically,UKGE-MS can improve the existing text mining technology's ability of understanding and discovering high-dimensional unmarked information,and solves the problems of traditional unsupervised feature selection methods,which only focus on selecting features from a global perspective and ignoring the impact of local connection of samples.Firstly,considering the influence of local information of samples in feature correlation evaluation,a feature clustering algorithm based on average neighborhood mutual information is proposed,and the feature clusters with certain event correlation are obtained;Secondly,an unsupervised feature selection method based on the high-order correlation of multi-dimensional statistical data is designed by combining the dimension reduction advantage of local linear embedding algorithm and the feature selection ability of sparse representation,so as to enhance the generalization ability of the selected feature items.Finally,the events knowledge graph is constructed by means of sparse representation and l1 norm.Extensive experiments are carried out on five real datasets and synthetic datasets,and the UKGE-MS are compared with five corresponding algorithms.The experimental results show that UKGE-MS is better than the traditional method in event clustering and feature selection,and has some advantages over other methods in text event recognition and discovery.

DOA Estimation Method Using Sparse Representation with Orthogonal Projection

In order to reduce the effect of noises on DOA estimation,this paper proposes a direc-tion-of-arrival(DOA)estimation method using sparse representation with orthogonal projection(OPSR).The OPSR method obtains a new covariance matrix by projecting the covariance matrix of the array data to the signal subspace,leading to the elimination of the noise subspace.After-wards,based on the new covariance matrix after the orthogonal projection,a new sparse representa-tion model is established and employed for DOA estimation.Simulation results demonstrate that compared to other methods,the OPSR method has higher angle resolution and better DOA estima-tion performance in the cases of few snapshots and low SNRs.

Human Mouth-State Recognition Based on Image Warping and Sparse Representation Combined with Homotopy

It is often necessary to recognize human mouth-states for detecting the number of audio sources and improving the speech recognition capability of an intelligent robot auditory system. A human mouth-state recognition method based on image warping and sparse representation( SR) combined with homotopy is proposed.Using properly warped training mouth-state images as atoms of the overcomplete dictionary overcomes the impact of the diversity of the mouths' scales,shapes and positions so that further improvement of the robustness can be achieved and the requirement for a large number of training samples can be relieved. The homotopy method is employed to compute the expansion coefficients effectively,i. e.,for sparse coding. The orthogonal matching pursuit( OMP) is also tested and compared with the homototy method. Experimental results and comparisons with the state-of-the-art methods have proved the effectiveness of the proposed approach.