Sparse Coefficients Research Articles

Sparse coding with morphology segmentation and multi-label fusion for hyperspectral image super-resolution

Hyperspectral image (HSI) super-solution to reconstruct high spatial resolution HSIs has attracted increasing interest in recent years. In this paper, we propose a HSI super-resolution framework based on sparse coding with morphology segmentation and multi-label fusion (MSML), which is composed of four stages: (1) A spectral dictionary is learned by the online dictionary learning approach from the given HSI; (2) The morphology segmentation technique is introduced to divide each multispectral image (MSI) band into a series of regions associated with a label map; (3) A weighted voting based multi-label fusion model is constructed to combine multiple label maps from MSI bands to determine 3-D patches; (4) A sparse coding model is built to calculate sparse coefficients of 3-D patches that are used for the HSI super-solution. Compared with traditional sparse representation based algorithms, the novel MSML method can more fully utilize the local spatial information of the MSI to realize the super-resolution, relying on the sparse coding on unfixed-size patches adaptively obtained by the morphology segmentation and multi-label fusion. The Indian Pines, Salinas, Botswana, and Pavia University datasets are used to evaluate the performance of our method. Experimental results indicate that the MSML achieves better super-resolution performance in contrast to state-of-the-art algorithms.

Effectively Clustering Single Cell RNA Sequencing Data by Sparse Representation.

Clustering analysis has been widely used in analyzing single-cell RNA-sequencing (scRNA-seq) data to study various biological problems at cellular level. Although a number of scRNA-seq data clustering methods have been developed, most of them evaluate the similarity of pairwise cells while ignoring the global relationships among cells, which sometimes cannot effectively capture the latent structure of cells. In this paper, we propose a new clustering method SPARC for scRNA-seq data. The most important feature of SPARC is a novel similarity metric that uses the sparse representation coefficients of each cell in terms of the other cells to measure the relationships among cells. In addition, we develop an outlier detection method to help parameter selection in SPARC. We compare SPARC with nine existing scRNA-seq data clustering methods on twelve real datasets. Experimental results show that SPARC achieves the state of the art performance. By further analyzing the cell similarity data derived from sparse representations, we find that SPARC is much more effective in mining high quality clusters of scRNA-seq data than two traditional similarity metrics. In conclusion, this study provides a new way to effectively cluster scRNA-seq data and achieves more accurate clustering results than the state of art methods.

Research on the Sparse Optimization Method of Periodic Weights and its Application in Bearing Fault Diagnosis

The vibration state monitoring signal of rolling bearings usually shows periodic transient impulse characteristics at the time of the fault, but in the fault sprouting stage and actual monitoring, its impulse components are easily disturbed by random pulses, harmonics, background noise, etc., which increases the difficulty of extracting the periodic shock characteristics of the fault. This paper proposed a rolling bearing fault feature extraction method based on sparse coefficient weighting theory and periodic enhancement strategy to effectively extract weak periodic shock features with a low signal-to-noise ratio. In the proposed period weighted sparse wavelet representation (PWSWR) method, firstly, based on the sparse wavelet model, the mean kurtosis (MK) index was introduced as a weight to distinguish the contribution of the wavelet coefficients of each signal component. Secondly, a sparse signal period enhancement strategy was proposed using the improved envelope harmonic product spectrum period estimation method. The strategy is embedded into the sparse representation model to achieve the periodic enhancement of filtered signals. Finally, the envelope detection of the sparse signal was carried out to identify the fault. The results of bearing fault simulation signals and two engineering test signals showed that the proposed method could effectively extract weak fault features of bearings and had certain advantages compared with other sparse methods.

Feature Extraction of Bearing Weak Fault Based on Sparse Coding Theory and Adaptive EWT

In industry, early fault signals of rolling bearings are submerged in strong background noise, causing a low signal-to-noise ratio (SNR) and difficult diagnosis. This paper proposes a fault feature extraction method based on an optimized Laplacian wavelet dictionary (LWD) and the feature symbol search (FSS) algorithm to extract early fault characteristic frequencies of bearings under low SNR. As the morphological parameters of the Laplace wavelet dictionary and sparse coefficients are not easy to obtain, this method uses the adaptive empirical wavelet transform (AEWT) to determine the morphological parameters of the Laplace wavelet. Firstly, AEWT is applied to obtain the different frequency components, and the combination index is utilized for optimal component selection. Then, the morphological parameters of LWD are determined by AEWT processing, by which the overcomplete dictionary that best matches the signal can be obtained. Finally, the optimal sparse representation of the component signal in the dictionary is calculated by FSS, which helps to achieve sparse denoising and enhance the impact features. The effectiveness of the method is verified by simulation. The effectiveness and advantages of LWDFSS-AEWT are verified by experiment in comparison with methods such as fast spectral kurtosis (FSK), correlation filtering (CF), shift-invariant sparse coding (SISC), base pursuit denoising (BPDN) and wavelet packet transform Kurtogram (WPT Kurtogram).

Time-frequency representation with reweighted regularization for fault diagnosis in a sparse way

In the field of fault diagnosis, time–frequency representation (TFR) is a very popular tool due to its good performance under time-varying condition. TFR provides both time and frequency information of fault signal, and the component related to fault characteristic frequency (FCF) can be found in the time–frequency image. To improve the time–frequency resolution of TFR, a special kind of TFR method named sparse time frequency representation (STFR) combines TFR and sparse theory, where the TFR is processed in a sparse way and the energy is more concentrated on FCF. However, the underestimation problem from the optimization process limits the efficiency of STFR. Concretely, the coefficients of the components of FCF are easy to be underestimated in the iterative process of solving coefficient, which will enhance other interference components. Especially for the weak faults from the early stage or the serious noise pollution, STFR is easy to be contaminated and is hard to reveal the components of FCF because of the underestimation problem. To solve the underestimation problem, we propose a novel STFR with reweighted regularization (RSTFR) for fault diagnosis. In the proposed method, the envelope of signal is divided into small segments, and each segment is decomposed into the Fourier basis. Naturally, the sparse coefficient represents the envelope spectrum of each segment. Meanwhile, the reweighted scheme is used to solve the underestimation problem. The components related to FCF are encouraged with low thresholds while other interference components are punished with high thresholds. At last, the envelope spectrums of all segments at different time form the TFR. The proposed method can provide a higher time–frequency resolution and diagnose the fault precisely. RSTFR is applied in the both simulation cases and experimental cases of bearing fault diagnosis, and it shows the overwhelming superiority compared to other four state-of-art TFR methods.

Hyperspectral image denoising and destriping based on sparse representation, graph Laplacian regularization and stripe low-rank property

During the acquisition of a hyperspectral image (HSI), it is easily corrupted by many kinds of noises, which limits the subsequent applications. For decades, numerous HSI denoising methods have been proposed. However, these methods rarely consider the stripe noise as an independent component, thus cannot effectively remove the stripe noise. In this paper, we propose a mixed noise removal algorithm to destripe an HSI by taking advantage of the low-rank property of stripe noise. In the meantime, sparse representation and graph Laplacian regularization are utilized to remove Gaussian and sparse noise. Roughly speaking, the sparse representation helps achieve the approximation of the original image. A graph Laplacian regularization term can ensure the non-local spatial similarity of an HSI. Separate constraints on the sparse coefficient matrix and stripe noise components can help remove different types of noises. Experimental results on both simulated and real data demonstrate the effectiveness of the proposed method for HSI restoration.

On-grid compressive sampling for spherical field measurements in acoustics.

We derive a compressive sampling method for acoustic field reconstruction using field measurements on a pre-defined spherical grid that has theoretically guaranteed relations between signal sparsity, measurement number, and reconstruction accuracy. This method can be used to reconstruct band limited spherical harmonic or Wigner D-function series (spherical harmonic series are a special case) with sparse coefficients. Contrasting typical compressive sampling methods for Wigner D-function series that use arbitrary random measurements, the new method samples randomly on an equiangular grid, a practical and commonly used sampling pattern. Using its periodic extension, we transform the reconstruction of a Wigner D-function series into a multi-dimensional Fourier domain reconstruction problem. We establish that this transformation has a bounded effect on sparsity level and provide numerical studies of this effect. We also compare the reconstruction performance of the new approach to classical Nyquist sampling and existing compressive sampling methods. In our tests, the new compressive sampling approach performs comparably to other guaranteed compressive sampling approaches and needs a fraction of the measurements dictated by the Nyquist sampling theorem. Moreover, using one-third of the measurements or less, the new compressive sampling method can provide over 20 dB better de-noising capability than oversampling with classical Fourier theory.

A No-Reference Quality Assessment Method for Screen Content Images Based on Human Visual Perception Characteristics

The widespread application of screen content images (SCIs) has met the needs of remote display and online working. It is a topic that is challenging and worthwhile discussing in research on quality assessment for SCIs. However, existing methods focus on extracting artificial features to predict image quality, which are subjective and incomplete, or lack good interpretability. To overcome these problems, we propose an effective quality assessment method for SCIs based on human visual perceptual characteristics. The proposed method simulates the multi-channel working mechanism of the human visual system (HVS) through pyramid decomposition and the information extraction process of brains with the help of dictionary learning and sparse coding. The input SCIs are first decomposed at multiple scales, and then dictionary learning and sparse coding are applied to the images at each scale. Furthermore, the sparse representation results are analyzed from multiple perspectives. First, a pooling scheme about generalized Gaussian distribution and log-normal distribution is designed to describe the sparse coefficients with and without zero values, respectively. Then the sparse coefficients are used to characterize the energy characteristics. Additionally, the probability of each atom is calculated to describe the statistical property of SCIs. Since the above process only deals with brightness, color-related features are also added to make the model more general and robust. Experimental results on three public SCI databases show that the proposed method can achieve better performance than existing methods.

Structured Sparse Coding With the Group Log-regularizer for Key Frame Extraction

Key frame extraction based on sparse coding can reduce the redundancy of continuous frames and concisely express the entire video. However, how to develop a key frame extraction algorithm that can automatically extract a few frames with a low reconstruction error remains a challenge. In this paper, we propose a novel model of structured sparse-coding-based key frame extraction, wherein a nonconvex group log-regularizer is used with strong sparsity and a low reconstruction error. To automatically extract key frames, a decomposition scheme is designed to separate the sparse coefficient matrix by rows. The rows enforced by the nonconvex group log-regularizer become zero or nonzero, leading to the learning of the structured sparse coefficient matrix. To solve the nonconvex problems due to the log-regularizer, the difference of convex algorithm (DCA) is employed to decompose the log-regularizer into the difference of two convex functions related to the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$I_{1}$</tex> norm, which can be directly obtained through the proximal operator. Therefore, an efficient structured sparse coding algorithm with the group log-regularizer for key frame extraction is developed, which can automatically extract a few frames directly from the video to represent the entire video with a low reconstruction error. Experimental results demonstrate that the proposed algorithm can extract more accurate key frames from most SumMe videos compared to the state-of-the-art methods. Furthermore, the proposed algorithm can obtain a higher compression with a nearly 18% increase compared to sparse modeling representation selection (SMRS) and an 8% increase compared to SC-det on the VSUMM dataset.

Sparse coefficient fast solution algorithm based on the circulant structure of a shift-invariant dictionary and its applications for machine fault diagnosis

Sparse coefficient solutions have received continuous attention as one of the core steps of sparse representation. The computational complexity of almost all sparse coefficient solution algorithms is exponentially increased with a signal dimension. In this paper, impact signals caused by localized faults are sparsely represented by a shift-invariant dictionary, which can be Fourier diagonalized based on its circulant structure. Then, the matrix–matrix and matrix–vector multiplications involved in obtaining sparse coefficients are converted into calculation forms that mainly contain the Fourier transform and its inverse to reduce computational complexity. Based on this result, fast solutions of three common sparse coefficient solution algorithms are deduced in detail. Simulation analysis shows that the deduced fast algorithms can significantly fasten running time while maintaining same accuracy as corresponding original algorithms. Localized rolling bearing faults related experiments further verify the effectiveness of the proposed sparse coefficient fast solution algorithms for machine fault diagnosis.

Signal Denoising of MEMS Vector Hydrophone Based on Optimized VMD, Compressed Sensing, and Wavelet Threshold

With the noise in underwater acoustic signal extracted from ocean background, the denoising algorithm based on the Variational Mode Decomposition (VMD) optimized by improved Grasshopper Optimization Algorithm (IGOA), the compressed sensing (CS) and wavelet threshold (WT) is proposed in this paper, named by IGOA-VMD-CS-WT, where VMD optimized by IGOA is utilized to perform sign composition and the obtained Intrinsic Mode Functions (IMF) are divided into effective components and noise components using cross-correlation coefficient of each IMF. CS is performed on sparse representation of noise components and the obtained sparse coefficients are processed with WT for the filters. The effective components and the denoised components are reconstructed to the denoised signal by the Orthogonal Matching Pursuit. The experiments show that IGOA-VMD-CS-WT has the highest signal-to-noise ratios and the least root mean square errors under different noise levels and has the better denoising effect on the denoising of the actual data.

SRNet: Sparse representation-based network for image denoising

Image denoising is a foundational but important task in image processing. Various traditional methods have been proposed to remove noise from noisy images. Sparse representation (SR) is a representative image denoising method. Although with good denoising effects, sparse representation suffers from performance bottlenecks and large time consumption. Recently, deep learning has demonstrated excellent ability in image denoising. Therefore, we consider combining the sparse representation with deep learning to make this traditional model more effective and efficient. The sparse representation-based network (SRNet) is proposed by embedding the convolutional neural network (CNN) into the sparse representation framework, in which all the parameters are learned by training. The iterative optimization process of sparse coding is unrolled into a network with several similar phases. In each phase, two subnetworks are designed with the multiscale residual block (MSR-block) to model the updating of sparse coefficient and image, respectively. The experimental results show that compared with the traditional sparse representation denoising methods, the proposed method can significantly reduce time consumption and improve denoising performance, especially in terms of reconstructing textures. The PyTorch code and models of the proposed SRNet can be released at https://github.com/JiechaoSheng/SRNet.

Deep side group sparse coding network for image denoising

Recently, deep learning has made significant progress in image denoising. However, most of existing deep learning based methods are purely data-driven, without considering the knowledge of image denoising. Moreover, the parameters of deep denoising network are not explainable. According to these issues, this paper proposes a deep side group sparse coding network for image denoising, named a side group sparse coding (SGSC)-Net. First, SGSC model for image denoising by exploiting prior information regarding the group sparse coefficients consistency is developed. Specifically, the side information is constructed as the weighted combination of intermediate estimations, and updated iteratively. Then, the optimisation solution of SGSC model is turned into a deep neural network using deep unfolding, that is, SGSC-Net. The computational path of SGSC-Net fully follows the iterations of optimisation solution, and consequently the network parameters are interpretable. Furthermore, the design of SGSC-Net employs the insight of SGSC denoising model. The experimental results on well-known datasets quantitatively and qualitatively demonstrate that SGSC-Net is competitive to existing deep unfolding-based and typical deep neural network-based methods.

Driving Fatigue Monitoring via Kernel Sparse Representation Regression With GMC Penalty

Automatic monitoring technology for fatigued driving can greatly reduce traffic accidents caused by drivers due to decreased attention. The use of monitoring algorithms based on physiological signal sensors is of great significance for objective monitoring. In this paper, a novel algorithm with excellent performance and strong generalization ability, kernel sparse representation regression based on generalized minimax-concave (GMC-KSRR), is proposed to identify fatigue physiological signals. Specifically, in the proposed algorithm, the training samples of physiological features are mapped in reproducing kernel Hilbert space (RKHS) for linear separability. Then, in RKHS, the sparse coefficients of the test samples are obtained by generalized minimax-concave (GMC) penalty-based sparse representation (SR). Different from the traditional <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{{1}}$ </tex-math></inline-formula> -norm, the GMC penalty we used does not underestimate the high-amplitude component of sparsity coefficients, resulting in a more accurate regression result. Finally, the regression decision is performed in the label subspace according to the obtained sparse coefficients. Meanwhile, a multimodality algorithm based on GMC-KSRR has also been proposed that weighs each modality according to quality for robust fatigue monitoring. Eventually, competitive experimental results on the well-known SEED-VIG dataset against the state-of-the-art methods demonstrate the efficacy of the proposed algorithms in identifying fatigue physiological signals, indicating its powerful application potential in driving fatigue monitoring.

An iterative framework to solve nonlinear optimal control with proportional delay using successive convexification and symplectic multi-interval pseudospectral scheme

In this paper, we propose an iterative framework to solve optimal control for nonlinear proportional state-delay systems. The successive convexification technique is first implemented to convert the original nonlinear problem into a sequence of linear-quadratic problems. And a symplectic pseudospectral method, where the multi-interval pseudospectral scheme is applied with a proportional mesh, to solve the transformed problems is then developed based on the first-order necessary conditions. Each linear-quadratic problem is finally transformed into a system of linear algebraic equations with a sparse coefficient matrix. Due to the benefit of the successive convexification technique and the multi-interval pseudospectral method, initial guess on costate variables is avoided and converged solutions can be obtained with an exponential convergent rate. The proposed iterative framework is validated by four examples with distinct features, highlighting its numerical precision and efficiency. And either exponential or linear convergence property can be exhibited by tuning the approximation degree or the mesh number.

Joint sparse model with coupled dictionary for medical image fusion

Medical image fusion has made great progress benefit from strong feature association ability of joint sparse model. Since medical images are obtained by different sensors with different imaging mechanisms, single dictionary cannot effectively characterize innovation and common information, which becomes stumbling block for effective fusion. In this paper, we propose novel joint sparse model with coupled dictionary learning for medical image fusion. Our framework design new fusion rule to enhance ability of multi-source signal preservation and retain edge/texture information. Firstly, source medical images was represented as a common sparse component and innovation sparse components with over-complete coupled dictionaries. Secondly, fused sparse coefficient is obtained by using the designed novel rule. Finally, fused results are reconstructed using fused coefficients and coupled dictionaries. Our proposed method is evaluated and compared with 9 state-of-the-art fusion methods on public Harvard dataset. Qualitative and quantitative results show that our method is generally better than the compared methods in terms of retaining source image structural and functional information.

Discriminative Convolutional Sparse Coding of ECG Signals for Automated Recognition of Cardiac Arrhythmias

Electrocardiogram (ECG) is a common and powerful tool for studying heart function and diagnosing several abnormal arrhythmias. In this paper, we present a novel classification model that combines the discriminative convolutional sparse coding (DCSC) framework with the linear support vector machine (LSVM) classification strategy. In the training phase, most existing convolutional sparse coding frameworks are unsupervised in the sense that label information is ignored in the convolutional filter training stage. In this work, we explicitly incorporate a label consistency constraint called “discriminative sparse-code error” into the objective function to learn discriminative dictionary filters for sparse coding. The learned dictionary filters encourage signals from the same class to have similar sparse codes, and signals from different classes to have dissimilar sparse codes. To reduce the computational complexity, we propose to perform a max-pooling operation on the sparse coefficients. Using LSVM as a classifier, we examine the performance of the proposed classification system on the MIT-BIH arrhythmia database in accordance with the AAMI EC57 standard. The experimental results show that the proposed DCSC + LSVM algorithm can obtain 99.32% classification accuracy for cardiac arrhythmia recognition.

Compressed sensing based fingerprint imaging system using a chaotic model-based deterministic sensing matrix

A secured compressed sensing (CS) systems design approach uses a novel deterministic sensing matrix to sense and transmit fingerprint images. The performance of the CS system was studied in detail by varying CS and security parameters. The sampling and sparse coefficient are the parameters considered from compressed sensing, whereas the encryption key is from the security scheme. The simultaneous compression and encryption has been achieved by multiplying the sparse modeled data with the proposed deterministic partial bounded orthogonal sensing matrix. A chaotic model-based permutation is applied to scramble the DCT matrix rows to build the sensing matrix. Recovering and decryption of the compressed image are accomplished with the help of the L1 optimization method. The experimental test shows that a sparse vector of 121 widths has been recovered by taking about 25 samples. This indicates that up to 1 : 5 compression ratio is supported without damaging the fingerprint minutiae. If only compression is required without encryption, up to a 1 : 16 ratio can be achieved. The peak signal-to-noise ratio (PSNR) is 27.65 dB for both compression ratios under fulfilments of all necessary security requirements. The 7.20 value of the entropy, histogram analysis, and the correlation analysis show the proposed scheme possesses adequate randomness. Furthermore, the ability of the system resistance against attacks is proved by 100% NPCR (Net Pixel Change Rate) and 0.92% UACI (Unified Average Changing Intensity) values.

Feature enhancing image inpainting through adaptive variation of sparse coefficients

Feature enhancing image inpainting through adaptive variation of sparse coefficients

Compressed feature reconstruction for localized fault diagnosis with generalized minimax-concave penalty

Compressed sensing can effectively relieve the burden of data storage and transmission for mechanical condition monitoring. However, feature reconstruction from compressed observations has always been a challenge. A novel compressed feature reconstruction method for the impulse response signal caused by localized damage is proposed based on the generalized minimax-concave (GMC) penalty. To improve the efficiency of compression and reconstruction, the fault signal is divided into several segments before compression, and the segmented sparse coefficient is obtained by solving a GMC problem. The fault-caused impulse signal is obtained by combining all the reconstructed segments together. Furthermore, a strategy of regularization parameter selection based on the sparse coefficient proxy is presented. Compared with the commonly used l1 regularization-based reconstruction method, the proposed method can better preserve the amplitudes of impulse features. The effectiveness of the proposed method is further verified by simulation and experimental data.