Compression techniques of mechanical vibration signals based on optimal sparse representations

This paper presents the result of an experimental study on the compression of mechanical vibration signals. The signals are collected from both rotating and reciprocating machineries by the accelerometers and a data acquisition （DAQ） system. Four optimal sparse representation methods for compression have been considered including the method of frames （ MOF）, best orthogonal basis （ BOB）, matching pursuit （MP） and basis pursuit （BP）. Furthermore, several indicators including compression ratio （CR）, mean square error （MSE）, energy retained （ER） and Kurtosis are taken to evaluate the performance of the above methods. Experimental results show that MP outperforms other three methods.

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.

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 Novel Clutter Suppression Algorithm for Low-Slow-Small Targets Detecting Based on Sparse Adaptive Filtering

Passive detection of low-slow-small(LSS)targets is easily interfered by direct signal and multipath clutter,and the traditional clutter suppression method has the contradiction between step size and convergence rate.In this paper,a frequency domain clutter suppression algorithm based on sparse adaptive filtering is proposed.The pulse compression operation between the error signal and the input reference signal is added to the cost function as a sparsity constraint,and the criterion for filter weight updating is improved to obtain a purer echo signal.At the same time,the step size and penalty factor are brought into the adaptive iteration process,and the input data is used to drive the adaptive changes of parameters such as step size.The proposed algorithm has a small amount of calculation,which improves the robustness to parameters such as step size,reduces the weight error of the filter and has a good clutter suppression performance.

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.

Sparse Representations-based depth images quality assessment

The conventional 2D metrics can be used for measuring the quality of depth maps,but none of them is considered to be efficient and is not accurate when used for evaluating 3D quality.In this paper,we propose a new full reference objective metric,called Sparse Representations-Mean Squared Error(SR-MSE),which efficiently evaluates the depth maps compression distortions.It adaptively models the reference and compressed depth maps in a mixed redundant transform domain dedicated to depth features.Then,it computes the mean squared error between the sparse coefficients issued from this modeling.As a benchmark of quality assessment,we perform a subjective evaluation test for depth maps compressed using the latest 3D High Efficiency Video Coding standard at various bitrates.We compare the subjective results with the proposed and conventional objective metrics.Experimental results demonstrate that the proposed SR-MSE,compared to the conventional image quality assessment metrics,yields the highest correlated scores to the subjective ones.

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.

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.

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.

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.

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.

Estimating High-Order Functional Connectivity Networks for Mild Cognitive Impairment Identification Based on Topological Structure

Functional connectivity networks (FCNs) are important in the diagnosis of neurological diseases and the understanding of brain tissue patterns. Recently, many methods, such as Pearson’s correlation (PC), Sparse representation (SR), and Sparse low-rank representation have been proposed to estimate FCNs. Despite their popularity, they only capture the low-order connections of the brain regions, failing to encode more complex relationships (i.e. , high-order relationships). Although researchers have proposed high-order methods, like PC + PC and SR + SR, aiming to build FCNs that can reflect more real state of the brain. However, such methods only consider the relationships between brain regions during the FCN construction process, neglecting the potential shared topological structure information between FCNs of different subjects. In addition, the low-order relationships are always neglected during the construction of high-order FCNs. To address these issues, in this paper we proposed a novel method, namely Ho-FCNTops, towards estimating high-order FCNs based on brain topological structure. Specifically, inspired by the Group-constrained sparse representation (GSR), we first introduced a prior assumption that all subjects share the same topological structure in the construction of the low-order FCNs. Subsequently, we employed the Correlation-reserved embedding (COPE) to eliminate noise and redundancy from the low-order FCNs. Meanwhile, we retained the original low-order relationships during the embedding process to obtain new node representations. Finally, we utilized the SR method on the obtained new node representations to construct the Ho-FCNTops required for disease identification. To validate the effectiveness of the proposed method, experiments were conducted on 137 subjects from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database to identify Mild Cognitive Impairment (MCI) patients from the normal controls. The experimental results demonstrate superior performance compared to baseline 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.

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.

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.

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.

Power-line interference suppression of MT data based on frequency domain sparse decomposition

Power-line interference is one of the most common noises in magnetotelluric(MT)data.It usually causes distortion at the fundamental frequency and its odd harmonics,and may also affect other frequency bands.Although trap circuits are designed to suppress such noise in most of the modern acquisition devices,strong interferences are still found in MT data,and the power-line interference will fluctuate with the changing of load current.The fixed trap circuits often fail to deal with it.This paper proposes an alternative scheme for power-line interference removal based on frequency-domain sparse decomposition.Firstly,the fast Fourier transform of the acquired MT signal is performed.Subsequently,a redundant dictionary is designed to match with the power-line interference which is insensitive to the useful signal.Power-line interference is separated by using the dictionary and a signal reconstruction algorithm of compressive sensing called improved orthogonal matching pursuit(IOMP).Finally,the frequency domain data are switched back to the time domain by the inverse fast Fourier transform.Simulation experiments and real data examples from Lu-Zong ore district illustrate that this scheme can effectively suppress the power-line interference and significantly improve data quality.Compared with time domain sparse decomposition,this scheme takes less time consumption and acquires better results.

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.

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.