SRMD:Sparse Random Mode Decomposition

Signal decomposition and multiscale signal analysis provide many useful tools for timefrequency analysis.We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram.The randomization is both in the time window locations and the frequency sampling,which lowers the overall sampling and computational cost.The sparsification of the spectrogram leads to a sharp separation between time-frequency clusters which makes it easier to identify intrinsic modes,and thus leads to a new data-driven mode decomposition.The applications include signal representation,outlier removal,and mode decomposition.On benchmark tests,we show that our approach outperforms other state-of-the-art decomposition methods.

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.

Physics-informed neural network-based petroleum reservoir simulation with sparse data using domain decomposition

Recent advances in deep learning have expanded new possibilities for fluid flow simulation in petroleum reservoirs.However,the predominant approach in existing research is to train neural networks using high-fidelity numerical simulation data.This presents a significant challenge because the sole source of authentic wellbore production data for training is sparse.In response to this challenge,this work introduces a novel architecture called physics-informed neural network based on domain decomposition(PINN-DD),aiming to effectively utilize the sparse production data of wells for reservoir simulation with large-scale systems.To harness the capabilities of physics-informed neural networks(PINNs)in handling small-scale spatial-temporal domain while addressing the challenges of large-scale systems with sparse labeled data,the computational domain is divided into two distinct sub-domains:the well-containing and the well-free sub-domain.Moreover,the two sub-domains and the interface are rigorously constrained by the governing equations,data matching,and boundary conditions.The accuracy of the proposed method is evaluated on two problems,and its performance is compared against state-of-the-art PINNs through numerical analysis as a benchmark.The results demonstrate the superiority of PINN-DD in handling large-scale reservoir simulation with limited data and show its potential to outperform conventional PINNs in such scenarios.

Application of sparse time-frequency decomposition to seismic data

The Gabor and S transforms are frequently used in time-frequency decomposition methods. Constrained by the uncertainty principle, both transforms produce low-resolution time-frequency decomposition results in the time and frequency domains. To improve the resolution of the time-frequency decomposition results, we use the instantaneous frequency distribution function（IFDF） to express the seismic signal. When the instantaneous frequencies of the nonstationary signal satisfy the requirements of the uncertainty principle, the support of IFDF is just the support of the amplitude ridges in the signal obtained using the short-time Fourier transform. Based on this feature, we propose a new iteration algorithm to achieve the sparse time-frequency decomposition of the signal. The iteration algorithm uses the support of the amplitude ridges of the residual signal obtained with the short-time Fourier transform to update the time-frequency components of the signal. The summation of the updated time-frequency components in each iteration is the result of the sparse timefrequency decomposition. Numerical examples show that the proposed method improves the resolution of the time-frequency decomposition results and the accuracy of the analysis of the nonstationary signal. We also use the proposed method to attenuate the ground roll of field seismic data with good results.

Gearbox Fault Diagnosis using Adaptive Zero Phase Time-varying Filter Based on Multi-scale Chirplet Sparse Signal Decomposition

When used for separating multi-component non-stationary signals, the adaptive time-varying filter(ATF) based on multi-scale chirplet sparse signal decomposition(MCSSD) generates phase shift and signal distortion. To overcome this drawback, the zero phase filter is introduced to the mentioned filter, and a fault diagnosis method for speed-changing gearbox is proposed. Firstly, the gear meshing frequency of each gearbox is estimated by chirplet path pursuit. Then, according to the estimated gear meshing frequencies, an adaptive zero phase time-varying filter(AZPTF) is designed to filter the original signal. Finally, the basis for fault diagnosis is acquired by the envelope order analysis to the filtered signal. The signal consisting of two time-varying amplitude modulation and frequency modulation(AM-FM) signals is respectively analyzed by ATF and AZPTF based on MCSSD. The simulation results show the variances between the original signals and the filtered signals yielded by AZPTF based on MCSSD are 13.67 and 41.14, which are far less than variances (323.45 and 482.86) between the original signals and the filtered signals obtained by ATF based on MCSSD. The experiment results on the vibration signals of gearboxes indicate that the vibration signals of the two speed-changing gearboxes installed on one foundation bed can be separated by AZPTF effectively. Based on the demodulation information of the vibration signal of each gearbox, the fault diagnosis can be implemented. Both simulation and experiment examples prove that the proposed filter can extract a mono-component time-varying AM-FM signal from the multi-component time-varying AM-FM signal without distortion.

Application of Atomic Sparse Decomposition to Feature Extraction of the Fault Signal in Small Current Grounding System

Applying the atomic sparse decomposition in the distribution network with harmonics and small current grounding to decompose the transient zero sequence current that appears after the single phase to ground fault occurred. Based on dictionary of Gabor atoms and matching pursuit algorithm, the method extracts the atomic components iteratively from the feature signals and translated them to damped sinusoidal components. Then we can obtain the parametrical and analytical representation of atomic components. The termination condition of decomposing iteration is determined by the threshold of the initial residual energy with the purpose of extract the features more effectively. Accordingly, the proposed method can extract the starting and ending moment of disturbances precisely as well as their magnitudes, frequencies and other features. The numerical examples demonstrate its effectiveness.

A bearing fault diagnosis method based on sparse decomposition theory

The bearing fault information is often interfered or lost in the background noise after the vibration signal being transferred complicatedly, which will make it very difficult to extract fault features from the vibration signals. To avoid the problem in choosing and extracting the fault features in bearing fault diagnosing, a novelty fault diagnosis method based on sparse decomposition theory is proposed. Certain over-complete dictionaries are obtained by training, on which the bearing vibration signals corresponded to different states can be decomposed sparsely. The fault detection and state identification can be achieved based on the fact that the sparse representation errors of the signal on different dictionaries are different. The effects of the representation error threshold and the number of dictionary atoms used in signal decomposition to the fault diagnosis are analyzed. The effectiveness of the proposed method is validated with experimental bearing vibration signals.

Denoising via truncated sparse decomposition

This paper proposes a denoising algorithm called truncated sparse decomposition （TSD） algorithm, which combines the advantage of the sparse decomposition with that of the minimum energy model truncation operation. Experimental results on two real chaotic signals show that the TSD algorithm outperforms the recently reported denoising algorithmsnon-negative sparse coding and singular value decomposition based method.

Chaotic signal denoising algorithm based on sparse decomposition

Denoising of chaotic signal is a challenge work due to its wide-band and noise-like characteristics.The algorithm should make the denoised signal have a high signal to noise ratio and retain the chaotic characteristics.We propose a denoising method of chaotic signals based on sparse decomposition and K-singular value decomposition(K-SVD)optimization.The observed signal is divided into segments and decomposed sparsely.The over-complete atomic library is constructed according to the differential equation of chaotic signals.The orthogonal matching pursuit algorithm is used to search the optimal matching atom.The atoms and coefficients are further processed to obtain the globally optimal atoms and coefficients by K-SVD.The simulation results show that the denoised signals have a higher signal to noise ratio and better preserve the chaotic characteristics.

Application of signal sparse decomposition in dynamic test

In dynamic test,sampling rate is high and noise is strong,so a signal sparse decomposition method based on Gabor dictionary is put forward.This method iteratively decomposes the signal with the matching pursuit(MP)algorithm and takes the coherence ratio of the threshold as a condition of iteration termination.Standard MP algorithm is time-consuming,thus an adaptive genetic algorithm is introduced to MP method,which makes computation speed accelerate effectively.Experimental results indicate that this method not only can effectively remove high-frequency noise but also can compress the signal greatly.

Robust least squares projection twin SVM and its sparse solution

Least squares projection twin support vector machine(LSPTSVM)has faster computing speed than classical least squares support vector machine(LSSVM).However,LSPTSVM is sensitive to outliers and its solution lacks sparsity.Therefore,it is difficult for LSPTSVM to process large-scale datasets with outliers.In this paper,we propose a robust LSPTSVM model(called R-LSPTSVM)by applying truncated least squares loss function.The robustness of R-LSPTSVM is proved from a weighted perspective.Furthermore,we obtain the sparse solution of R-LSPTSVM by using the pivoting Cholesky factorization method in primal space.Finally,the sparse R-LSPTSVM algorithm(SR-LSPTSVM)is proposed.Experimental results show that SR-LSPTSVM is insensitive to outliers and can deal with large-scale datasets fastly.

Refined Sparse Representation Based Similar Category Image Retrieval

Given one specific image,it would be quite significant if humanity could simply retrieve all those pictures that fall into a similar category of images.However,traditional methods are inclined to achieve high-quality retrieval by utilizing adequate learning instances,ignoring the extraction of the image’s essential information which leads to difficulty in the retrieval of similar category images just using one reference image.Aiming to solve this problem above,we proposed in this paper one refined sparse representation based similar category image retrieval model.On the one hand,saliency detection and multi-level decomposition could contribute to taking salient and spatial information into consideration more fully in the future.On the other hand,the cross mutual sparse coding model aims to extract the image’s essential feature to the maximumextent possible.At last,we set up a database concluding a large number of multi-source images.Adequate groups of comparative experiments show that our method could contribute to retrieving similar category images effectively.Moreover,adequate groups of ablation experiments show that nearly all procedures play their roles,respectively.

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.

Proximity point algorithm for low-rank matrix recovery from sparse noise corrupted data

The method of recovering a low-rank matrix with an unknown fraction whose entries are arbitrarily corrupted is known as the robust principal component analysis （RPCA）. This RPCA problem, under some conditions, can be exactly solved via convex optimization by minimizing a combination of the nuclear norm and the 11 norm. In this paper, an algorithm based on the Douglas-Rachford splitting method is proposed for solving the RPCA problem. First, the convex optimization problem is solved by canceling the constraint of the variables, and ~hen the proximity operators of the objective function are computed alternately. The new algorithm can exactly recover the low-rank and sparse components simultaneously, and it is proved to be convergent. Numerical simulations demonstrate the practical utility of the proposed algorithm.

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.

Extraction method of typical IEQ spatial distributions based on low-rank sparse representation and multi-step clustering

Indoor environment quality(IEQ)is one of the most concerned building performances during the operation stage.The non-uniform spatial distribution of various IEQ parameters in large-scale public buildings has been demonstrated to be an essential factor affecting occupant comfort and building energy consumption.Currently,IEQ sensors have been widely employed in buildings to monitor thermal,visual,acoustic and air quality.However,there is a lack of effective methods for exploring the typical spatial distribution of indoor environmental quality parameters,which is crucial for assessing and controlling non-uniform indoor environments.In this study,a novel clustering method for extracting IEQ spatial distribution patterns is proposed.Firstly,representation vectors reflecting IEQ distributions in the concerned space are generated based on the low-rank sparse representation.Secondly,a multi-step clustering method,which addressed the problems of the“curse of dimensionality”,is designed to obtain typical IEQ distribution patterns of the entire indoor space.The proposed method was applied to the analysis of indoor thermal environment in Beijing Daxing international airport terminal.As a result,four typical temperature spatial distribution patterns of the terminal were extracted from a four-month monitoring,which had been validated for their good representativeness.These typical patterns revealed typical environmental issues in the terminal,such as long-term localized overheating and temperature increases due to a sudden influx of people.The extracted typical IEQ spatial distribution patterns could assist building operators in effectively assessing the uneven distribution of IEQ space under current environmental conditions,facilitating targeted environmental improvements,optimization of thermal comfort levels,and application of energy-saving measures.

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.

DOA ESTIMATION USING A SPARSE LINEAR MODEL BASED ON EIGENVECTORS

To reduce high computational cost of existing Direction-Of-Arrival(DOA) estimation techniques within a sparse representation framework,a novel method with low computational com-plexity is proposed.Firstly,a sparse linear model constructed from the eigenvectors of covariance matrix of array received signals is built.Then based on the FOCal Underdetermined System Solver(FOCUSS) algorithm,a sparse solution finding algorithm to solve the model is developed.Compared with other state-of-the-art methods using a sparse representation,our approach also can resolve closely and highly correlated sources without a priori knowledge of the number of sources.However,our method has lower computational complexity and performs better in low Signal-to-Noise Ratio(SNR).Lastly,the performance of the proposed method is illustrated by computer simulations.

Truncated sparse approximation property and truncated q-norm minimization

This paper considers approximately sparse signal and low-rank matrix’s recovery via truncated norm minimization minx∥xT∥q and minX∥XT∥Sq from noisy measurements.We first introduce truncated sparse approximation property,a more general robust null space property,and establish the stable recovery of signals and matrices under the truncated sparse approximation property.We also explore the relationship between the restricted isometry property and truncated sparse approximation property.And we also prove that if a measurement matrix A or linear map A satisfies truncated sparse approximation property of order k,then the first inequality in restricted isometry property of order k and of order 2k can hold for certain different constantsδk andδ2k,respectively.Last,we show that ifδs(k+|T^c|)<√(s-1)/s for some s≥4/3,then measurement matrix A and linear map A satisfy truncated sparse approximation property of order k.It should be pointed out that when Tc=Ф,our conclusion implies that sparse approximation property of order k is weaker than restricted isometry property of order sk.