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.

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 Disturbance Localization Method for Power System Based on Group Sparse Representation and Entropy Weight Method

This paper addresses the problem of complex and challenging disturbance localization in the current power system operation environment by proposing a disturbance localization method for power systems based on group sparse representation and entropy weight method.Three different electrical quantities are selected as observations in the compressed sensing algorithm.The entropy weighting method is employed to calculate the weights of different observations based on their relative disturbance levels.Subsequently,by leveraging the topological information of the power system and pre-designing an overcomplete dictionary of disturbances based on the corresponding system parameter variations caused by disturbances,an improved Joint Generalized Orthogonal Matching Pursuit(J-GOMP)algorithm is utilized for reconstruction.The reconstructed sparse vectors are divided into three parts.If at least two parts have consistent node identifiers,the node is identified as the disturbance node.If the node identifiers in all three parts are inconsistent,further analysis is conducted considering the weights to determine the disturbance node.Simulation results based on the IEEE 39-bus system model demonstrate that the proposed method,utilizing electrical quantity information from only 8 measurement points,effectively locates disturbance positions and is applicable to various disturbance types with strong noise resistance.

Hyperspectral image classification based on spatial and spectral features and sparse representation

To minimize the low classification accuracy and low utilization of spatial information in traditional hyperspectral image classification methods, we propose a new hyperspectral image classification method, which is based on the Gabor spatial texture features and nonparametric weighted spectral features, and the sparse representation classification method（Gabor–NWSF and SRC）, abbreviated GNWSF–SRC. The proposed（GNWSF–SRC） method first combines the Gabor spatial features and nonparametric weighted spectral features to describe the hyperspectral image, and then applies the sparse representation method. Finally, the classification is obtained by analyzing the reconstruction error. We use the proposed method to process two typical hyperspectral data sets with different percentages of training samples. Theoretical analysis and simulation demonstrate that the proposed method improves the classification accuracy and Kappa coefficient compared with traditional classification methods and achieves better classification performance.

Low-Rank Sparse Representation with Pre-Learned Dictionaries and Side Information for Singing Voice Separation

At present, although the human speech separation has achieved fruitful results, it is not ideal for the separation of singing and accompaniment. Based on low-rank and sparse optimization theory, in this paper, we propose a new singing voice separation algorithm called Low-rank, Sparse Representation with pre-learned dictionaries and side Information (LSRi). The algorithm incorporates both the vocal and instrumental spectrograms as sparse matrix and low-rank matrix, meanwhile combines pre-learning dictionary and the reconstructed voice spectrogram form the annotation. Evaluations on the iKala dataset show that the proposed methods are effective and efficient for singing voice separation.

Low-Rank Multi-View Subspace Clustering Based on Sparse Regularization

Multi-view Subspace Clustering (MVSC) emerges as an advanced clustering method, designed to integrate diverse views to uncover a common subspace, enhancing the accuracy and robustness of clustering results. The significance of low-rank prior in MVSC is emphasized, highlighting its role in capturing the global data structure across views for improved performance. However, it faces challenges with outlier sensitivity due to its reliance on the Frobenius norm for error measurement. Addressing this, our paper proposes a Low-Rank Multi-view Subspace Clustering Based on Sparse Regularization (LMVSC- Sparse) approach. Sparse regularization helps in selecting the most relevant features or views for clustering while ignoring irrelevant or noisy ones. This leads to a more efficient and effective representation of the data, improving the clustering accuracy and robustness, especially in the presence of outliers or noisy data. By incorporating sparse regularization, LMVSC-Sparse can effectively handle outlier sensitivity, which is a common challenge in traditional MVSC methods relying solely on low-rank priors. Then Alternating Direction Method of Multipliers (ADMM) algorithm is employed to solve the proposed optimization problems. Our comprehensive experiments demonstrate the efficiency and effectiveness of LMVSC-Sparse, offering a robust alternative to traditional MVSC methods.

Robust Principal Component Analysis Integrating Sparse and Low-Rank Priors

Principal Component Analysis (PCA) is a widely used technique for data analysis and dimensionality reduction, but its sensitivity to feature scale and outliers limits its applicability. Robust Principal Component Analysis (RPCA) addresses these limitations by decomposing data into a low-rank matrix capturing the underlying structure and a sparse matrix identifying outliers, enhancing robustness against noise and outliers. This paper introduces a novel RPCA variant, Robust PCA Integrating Sparse and Low-rank Priors (RPCA-SL). Each prior targets a specific aspect of the data’s underlying structure and their combination allows for a more nuanced and accurate separation of the main data components from outliers and noise. Then RPCA-SL is solved by employing a proximal gradient algorithm for improved anomaly detection and data decomposition. Experimental results on simulation and real data demonstrate significant advancements.

Multi-Modal Medical Image Fusion Based on Improved Parameter Adaptive PCNN and Latent Low-Rank Representation

Multimodal medical image fusion can help physicians provide more accurate treatment plans for patients, as unimodal images provide limited valid information. To address the insufficient ability of traditional medical image fusion solutions to protect image details and significant information, a new multimodality medical image fusion method(NSST-PAPCNNLatLRR) is proposed in this paper. Firstly, the high and low-frequency sub-band coefficients are obtained by decomposing the source image using NSST. Then, the latent low-rank representation algorithm is used to process the low-frequency sub-band coefficients;An improved PAPCNN algorithm is also proposed for the fusion of high-frequency sub-band coefficients. The improved PAPCNN model was based on the automatic setting of the parameters, and the optimal method was configured for the time decay factor αe. The experimental results show that, in comparison with the five mainstream fusion algorithms, the new algorithm has significantly improved the visual effect over the comparison algorithm,enhanced the ability to characterize important information in images, and further improved the ability to protect the detailed information;the new algorithm has achieved at least four firsts in six objective indexes.

Infrared small target detection using sparse representation

Sparse representation has recently been proved to be a powerful tool in image processing and object recognition.This paper proposes a novel small target detection algorithm based on this technique.By modelling a small target as a linear combination of certain target samples and then solving a sparse 0-minimization problem,the proposed apporach successfully improves and optimizes the small target representation with innovation.Furthermore,the sparsity concentration index（SCI） is creatively employed to evaluate the coefficients of each block representation and simpfy target identification.In the detection frame,target samples are firstly generated to constitute an over-complete dictionary matrix using Gaussian intensity model（GIM）,and then sparse model solvers are applied to finding sparse representation for each sub-image block.Finally,SCI lexicographical evalution of the entire image incorparates with a simple threshold locate target position.The effectiveness and robustness of the proposed algorithm are demonstrated by the exprimental results.

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.

Weighted Sparse Image Classification Based on Low Rank Representation

The conventional sparse representation-based image classification usually codes the samples independently,which will ignore the correlation information existed in the data.Hence,if we can explore the correlation information hidden in the data,the classification result will be improved significantly.To this end,in this paper,a novel weighted supervised spare coding method is proposed to address the image classification problem.The proposed method firstly explores the structural information sufficiently hidden in the data based on the low rank representation.And then,it introduced the extracted structural information to a novel weighted sparse representation model to code the samples in a supervised way.Experimental results show that the proposed method is superiority to many conventional image classification methods.

Sparse representation-based color visualization method for hyperspectral imaging

In this paper, we designed a color visualization model for sparse representation of the whole hyperspectral image, in which, not only the spectral information in the sparse representation but also the spatial information of the whole image is retained. After the sparse representation, the color labels of the effective elements of the sparse coding dictionary are selected according to the sparse coefficient and then the mixed images are displayed. The generated images maintain spectral distance preservation and have good separability. For local ground objects, the proposed single-pixel mixed array and improved oriented sliver textures methods are integrated to display the specific composition of each pixel. This avoids the confusion of the color presentation in the mixed-pixel color display and can also be used to reconstruct the original hyperspectral data. Finally, the model effectiveness was proved using real data. This method is promising and can find use in many fields, such as energy exploration, environmental monitoring, disaster warning, and so on.

Underdetermined DOA estimation and blind separation of non-disjoint sources in time-frequency domain based on sparse representation method

This paper deals with the blind separation of nonstation-ary sources and direction-of-arrival （DOA） estimation in the under-determined case, when there are more sources than sensors. We assume the sources to be time-frequency （TF） disjoint to a certain extent. In particular, the number of sources presented at any TF neighborhood is strictly less than that of sensors. We can identify the real number of active sources and achieve separation in any TF neighborhood by the sparse representation method. Compared with the subspace-based algorithm under the same sparseness assumption, which suffers from the extra noise effect since it can-not estimate the true number of active sources, the proposed algorithm can estimate the number of active sources and their cor-responding TF values in any TF neighborhood simultaneously. An-other contribution of this paper is a new estimation procedure for the DOA of sources in the underdetermined case, which combines the TF sparseness of sources and the clustering technique. Sim-ulation results demonstrate the validity and high performance of the proposed algorithm in both blind source separation （BSS） and DOA estimation.

DOA estimation of coexisted noncoherent and coherent signals via sparse representation of cleaned array covariance matrix

A new direction finding method is presented to deal with coexisted noncoherent and co- herent signals without smoothing operation. First the direction-of-arrival （DOA） estimation task is herein reformulated as a sparse reconstruction problem of the cleaned array covariance matrix, which is processed to eliminate the affection of the noise. Then by using the block of matrices, the information of DOAs which we pursuit are implied in the sparse coefficient matrix. Finally, the sparse reconstruction problem is solved by the improved M-FOCUSS method, which is applied to the situation of block of matrices. This method outperforms its data domain counterpart in terms of noise suppression, and has a better performance in DOA estimation than the customary spatial smoothing technique. Simulation results verify the efficacy of the proposed method.

Single frame super-resolution reconstruction based on sparse representation

In order to effectively improve the quality of recovered images, a single frame super-resolution reconstruction method based on sparse representation is proposed. The combination method of local orientation estimation-based image patch clustering and principal component analysis is used to obtain a series of geometric dictionaries of different orientations in the dictionary learning process. Subsequently, the dictionary of the nearest orientation is adaptively assigned to each of the input patches that need to be represented in the sparse coding process. Moreover, the consistency of gradients is further incorporated into the basic framework to make more substantial progress in preserving more fine edges and producing sharper results. Two groups of experiments on different types of natural images indicate that the proposed method outperforms some state-of- the-art counterparts in terms of both numerical indicators and visual quality.

Fast image super-resolution algorithm based on multi-resolution dictionary learning and sparse representation

Sparse representation has attracted extensive attention and performed well on image super-resolution（SR） in the last decade. However, many current image SR methods face the contradiction of detail recovery and artifact suppression. We propose a multi-resolution dictionary learning（MRDL） model to solve this contradiction, and give a fast single image SR method based on the MRDL model. To obtain the MRDL model, we first extract multi-scale patches by using our proposed adaptive patch partition method（APPM）. The APPM divides images into patches of different sizes according to their detail richness. Then, the multiresolution dictionary pairs, which contain structural primitives of various resolutions, can be trained from these multi-scale patches.Owing to the MRDL strategy, our SR algorithm not only recovers details well, with less jag and noise, but also significantly improves the computational efficiency. Experimental results validate that our algorithm performs better than other SR methods in evaluation metrics and visual perception.

Pre-detection and dual-dictionary sparse representation based face recognition algorithm in non-sufficient training samples

Face recognition based on few training samples is a challenging task. In daily applications, sufficient training samples may not be obtained and most of the gained training samples are in various illuminations and poses. Non-sufficient training samples could not effectively express various facial conditions, so the improvement of the face recognition rate under the non-sufficient training samples condition becomes a laborious mission. In our work, the facial pose pre-recognition(FPPR) model and the dualdictionary sparse representation classification(DD-SRC) are proposed for face recognition. The FPPR model is based on the facial geometric characteristic and machine learning, dividing a testing sample into full-face and profile. Different poses in a single dictionary are influenced by each other, which leads to a low face recognition rate. The DD-SRC contains two dictionaries, full-face dictionary and profile dictionary, and is able to reduce the interference. After FPPR, the sample is processed by the DD-SRC to find the most similar one in training samples. The experimental results show the performance of the proposed algorithm on olivetti research laboratory(ORL) and face recognition technology(FERET) databases, and also reflect comparisons with SRC, linear regression classification(LRC), and two-phase test sample sparse representation(TPTSSR).

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.

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.

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%.