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Journal articles on the topic 'Sparse signal'

Author: Grafiati

Published: 4 June 2021

Last updated: 10 February 2022

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1

Mingjiang Shi, Xiaoyan Zhuang, and He Zhang. "Signal Reconstruction for Frequency Sparse Sampling Signals." Journal of Convergence Information Technology 8, no. 9 (May 15, 2013): 1197–203. http://dx.doi.org/10.4156/jcit.vol8.issue9.147.

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2

Peng, Wei, Dong Wang, Changqing Shen, and Dongni Liu. "Sparse Signal Representations of Bearing Fault Signals for Exhibiting Bearing Fault Features." Shock and Vibration 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/1835127.

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Sparse signal representations attract much attention in the community of signal processing because only a few coefficients are required to represent a signal and these coefficients make the signal understandable. For bearing faults’ diagnosis, bearing faults signals collected from transducers are often overwhelmed by strong low-frequency periodic signals and heavy noises. In this paper, a joint signal processing method is proposed to extract sparse envelope coefficients, which are the sparse signal representations of bearing fault signals. Firstly, to enhance bearing fault signals, particle swarm optimization is introduced to tune the parameters of wavelet transform and the optimal wavelet transform is used for retaining one of the resonant frequency bands. Thus, sparse wavelet coefficients are obtained. Secondly, to reduce the in-band noises existing in the sparse wavelet coefficients, an adaptive morphological analysis with an iterative local maximum detection method is developed to extract sparse envelope coefficients. Simulated and real bearing fault signals are investigated to illustrate how the sparse envelope coefficients are extracted. The results show that the sparse envelope coefficients can be used to represent bearing fault features and identify different localized bearing faults.

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3

Wang, Tianjing, Hang Shen, Xiaomei Zhu, Guoqing Liu, and Hua Jiang. "An Adaptive Gradient Projection Algorithm for Piecewise Convex Optimization and Its Application in Compressed Spectrum Sensing." Mathematical Problems in Engineering 2018 (2018): 1–9. http://dx.doi.org/10.1155/2018/9547934.

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Signal sparse representation has attracted much attention in a wide range of application fields. A central aim of signal sparse representation is to find a sparse solution with the fewest nonzero entries from an underdetermined linear system, which leads to various optimization problems. In this paper, we propose an Adaptive Gradient Projection (AGP) algorithm to solve the piecewise convex optimization in signal sparse representation. To find a sparser solution, AGP provides an adaptive stepsize to move the iteration solution out of the attraction basin of a suboptimal sparse solution and enter the attraction basin of a sparser solution. Theoretical analyses are used to show its fast convergence property. The experimental results of real-world applications in compressed spectrum sensing show that AGP outperforms the traditional detection algorithms in low signal-to-noise-ratio environments.

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4

Vujović, Stefan, Andjela Draganić, Maja Lakičević Žarić, Irena Orović, Miloš Daković, Marko Beko, and Srdjan Stanković. "Sparse Analyzer Tool for Biomedical Signals." Sensors 20, no. 9 (May 2, 2020): 2602. http://dx.doi.org/10.3390/s20092602.

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The virtual (software) instrument with a statistical analyzer for testing algorithms for biomedical signals’ recovery in compressive sensing (CS) scenario is presented. Various CS reconstruction algorithms are implemented with the aim to be applicable for different types of biomedical signals and different applications with under-sampled data. Incomplete sampling/sensing can be considered as a sort of signal damage, where missing data can occur as a result of noise or the incomplete signal acquisition procedure. Many approaches for recovering the missing signal parts have been developed, depending on the signal nature. Here, several approaches and their applications are presented for medical signals and images. The possibility to analyze results using different statistical parameters is provided, with the aim to choose the most suitable approach for a specific application. The instrument provides manifold possibilities such as fitting different parameters for the considered signal and testing the efficiency under different percentages of missing data. The reconstruction accuracy is measured by the mean square error (MSE) between original and reconstructed signal. Computational time is important from the aspect of power requirements, thus enabling the selection of a suitable algorithm. The instrument contains its own signal database, but there is also the possibility to load any external data for analysis.

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Xuan Liu, Xuan Liu, and Jin U. Kang Jin U. Kang. "Iterative sparse reconstruction of spectral domain OCT signal." Chinese Optics Letters 12, no. 5 (2014): 051701–51704. http://dx.doi.org/10.3788/col201412.051701.

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6

Ye, Chen, Guan Gui, Shin-ya Matsushita, and Li Xu. "Block Sparse Signal Reconstruction Using Block-Sparse Adaptive Filtering Algorithms." Journal of Advanced Computational Intelligence and Intelligent Informatics 20, no. 7 (December 20, 2016): 1119–26. http://dx.doi.org/10.20965/jaciii.2016.p1119.

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Sparse signal reconstruction (SSR) problems based on compressive sensing (CS) arise in a broad range of application fields. Among these are the so-called “block-structured” or “block sparse” signals with nonzero atoms occurring in clusters that occur frequently in natural signals. To make block-structured sparsity use more explicit, many block-structure-based SSR algorithms, such as convex optimization and greedy pursuit, have been developed. Convex optimization algorithms usually pose a heavy computational burden, while greedy pursuit algorithms are overly sensitive to ambient interferences, so these two types of block-structure-based SSR algorithms may not be suited for solving large-scale problems in strong interference scenarios. Sparse adaptive filtering algorithms have recently been shown to solve large-scale CS problems effectively for conventional vector sparse signals. Encouraged by these facts, we propose two novel block-structure-based sparse adaptive filtering algorithms, i.e., the “block zero attracting least mean square” (BZA-LMS) algorithm and the “block&ell;0-norm LMS” (BL0-LMS) algorithm, to exploit their potential performance gain. Experimental results presented demonstrate the validity and applicability of these proposed algorithms.

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7

Selesnick, Ivan W., and Ilker Bayram. "Sparse Signal Estimation by Maximally Sparse Convex Optimization." IEEE Transactions on Signal Processing 62, no. 5 (March 2014): 1078–92. http://dx.doi.org/10.1109/tsp.2014.2298839.

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8

Wand, Weidong, Qunfei Zhang, Wentao Shi, Juan SHI, Weijie Tan, and Xuhu Wang. "Iterative Sparse Covariance Matrix Fitting Direction of Arrival Estimation Method Based on Vector Hydrophone Array." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 38, no. 1 (February 2020): 14–23. http://dx.doi.org/10.1051/jnwpu/20203810014.

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Aiming at the direction of arrival (DOA) estimation of coherent signals in vector hydrophone array, an iterative sparse covariance matrix fitting algorithm is proposed. Based on the fitting criterion of weighted covariance matrix, the objective function of sparse signal power is constructed, and the recursive formula of sparse signal power iteration updating is deduced by using the properties of Frobenius norm. The present algorithm uses the idea of iterative reconstruction to calculate the power of signals on discrete grids, so that the estimated power is more accurate, and thus more accurate DOA estimation can be obtained. The theoretical analysis shows that the power of the signal at the grid point solved by the present algorithm is preprocessed by a filter, which allows signals in specified directions to pass through and attenuate signals in other directions, and has low sensitivity to the correlation of signals. The simulation results show that the average error estimated by the present method is 39.4% of the multi-signal classification high resolution method and 73.7% of the iterative adaptive sparse signal representation method when the signal-to-noise ratio is 15 dB and the non-coherent signal. Moreover, the average error estimated by the present method is 12.9% of the iterative adaptive sparse signal representation method in the case of coherent signal. Therefore, the present algorithm effectively improves the accuracy of target DOA estimation when applying to DOA estimation with highly correlated targets.

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9

Zhao, Shengjie, Jianchen Zhu, and Di Wu. "Design and Application of a Greedy Pursuit Algorithm Adapted to Overcomplete Dictionary for Sparse Signal Recovery." Traitement du Signal 37, no. 5 (November 25, 2020): 723–32. http://dx.doi.org/10.18280/ts.370504.

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Compressive sensing (CS) is a novel paradigm to recover a sparse signal in compressed domain. In some overcomplete dictionaries, most practical signals are sparse rather than orthonormal. Signal space greedy method can derive the optimal or near-optimal projections, making it possible to identify a few most relevant dictionary atoms of an arbitrary signal. More practically, such projections can be processed by standard CS recovery algorithms. This paper proposes a signal space subspace pursuit (SSSP) method to compute spare signal representations with overcomplete dictionaries, whenever the sensing matrix satisfies the restricted isometry property adapted to dictionary (D-RIP). Specifically, theoretical guarantees were provided to recover the signals from their measurements with overwhelming probability, as long as the sensing matrix satisfies the D-RIP. In addition, a thorough analysis was performed to minimize the number of measurements required for such guarantees. Simulation results demonstrate the validity of our hypothetical theory, as well as the superiority of the proposed approach.

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10

Song, Heping, and Guoli Wang. "Sparse Signal Recovery via ECME Thresholding Pursuits." Mathematical Problems in Engineering 2012 (2012): 1–22. http://dx.doi.org/10.1155/2012/478931.

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The emerging theory of compressive sensing (CS) provides a new sparse signal processing paradigm for reconstructing sparse signals from the undersampled linear measurements. Recently, numerous algorithms have been developed to solve convex optimization problems for CS sparse signal recovery. However, in some certain circumstances, greedy algorithms exhibit superior performance than convex methods. This paper is a followup to the recent paper of Wang and Yin (2010), who refine BP reconstructions via iterative support detection (ISD). The heuristic idea of ISD was applied to greedy algorithms. We developed two approaches for accelerating the ECME iteration. The described algorithms, named ECME thresholding pursuits (EMTP), introduced two greedy strategies that each iteration detects a support setIby thresholding the result of the ECME iteration and estimates the reconstructed signal by solving a truncated least-squares problem on the support setI. Two effective support detection strategies are devised for the sparse signals with components having a fast decaying distribution of nonzero components. The experimental studies are presented to demonstrate that EMTP offers an appealing alternative to state-of-the-art algorithms for sparse signal recovery.

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11

Luo, Ying, Qun Zhang, Guozheng Wang, and Youqing Bai. "Exact CS Reconstruction Condition of Undersampled Spectrum-Sparse Signals." Journal of Applied Mathematics 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/715848.

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Compressive sensing (CS) reconstruction of a spectrum-sparse signal from undersampled data is, in fact, an ill-posed problem. In this paper, we mathematically prove that, in certain cases, the exact CS reconstruction of a spectrum-sparse signal from undersampled data is impossible. Then we present the exact CS reconstruction condition of undersampled spectrum-sparse signals, which is valuable for digital signal compression.

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12

Xia, Yu, and Song Li. "Nonuniform recovery of fusion frame structured sparse signals." Analysis and Applications 15, no. 03 (April 18, 2017): 333–52. http://dx.doi.org/10.1142/s0219530516500032.

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This paper considers the nonuniform sparse recovery of block signals in a fusion frame, which is a collection of subspaces that provides redundant representation of signal spaces. Combined with specific fusion frame, the sensing mechanism selects block-vector-valued measurements independently at random from a probability distribution [Formula: see text]. If the probability distribution [Formula: see text] obeys a simple incoherence property and an isotropy property, we can faithfully recover approximately block sparse signals via mixed [Formula: see text]-minimization in ways similar to Compressed Sensing. The number of measurements is significantly reduced by a priori knowledge of a certain incoherence parameter [Formula: see text] associated with the angles between the fusion frame subspaces. As an example, the paper shows that an [Formula: see text]-sparse block signal can be exactly recovered from about [Formula: see text] Fourier coefficients combined with fusion frame [Formula: see text], where [Formula: see text].

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13

Rosenthal, A., D. Razansky, and V. Ntziachristos. "Quantitative Optoacoustic Signal Extraction Using Sparse Signal Representation." IEEE Transactions on Medical Imaging 28, no. 12 (December 2009): 1997–2006. http://dx.doi.org/10.1109/tmi.2009.2027116.

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14

Guo, Jun Feng, Xiao Hui Zheng, Xing Chun Wei, and Rui Cheng Feng. "Sparse Representation of Vibration Signals Using Trained Dictionary." Applied Mechanics and Materials 574 (July 2014): 690–95. http://dx.doi.org/10.4028/www.scientific.net/amm.574.690.

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The sparsity of a signal is critical for compression and high compression performance is obtained by utterly sparse signal. But real signals are not sparse commonly, so sparse transformation is considered. In addition, the sparse degree of coefficients is mainly determined by the quality of transform base. Therefore, this paper constructs a transform base (trained dictionary) by K-SVD algorithm for rolling element bearing vibration signals and uses the Orthogonal Matching Pursuit (OMP) algorithm to conduct sparse representation and simulation. Results show that the trained dictionary can be more fitted with the features of signals, the residual components are smaller and the reconstruct similarity is higher compared to the untrained dictionaries, obtaining better representation.

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15

Fletcher, A. K., S. Rangan, and V. K. Goyal. "Ranked Sparse Signal Support Detection." IEEE Transactions on Signal Processing 60, no. 11 (November 2012): 5919–31. http://dx.doi.org/10.1109/tsp.2012.2208957.

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16

Blu, T., P. L. Dragotti, M. Vetterli, P. Marziliano, and L. Coulot. "Sparse Sampling of Signal Innovations." IEEE Signal Processing Magazine 25, no. 2 (March 2008): 31–40. http://dx.doi.org/10.1109/msp.2007.914998.

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17

Gao, Guang Chun, Kai Xiong, Li Na Shang, Sheng Ying Zhao, and Cui Zhang. "Study on Over-Complete Dictionaries for Sparse Representations of Signals." Applied Mechanics and Materials 157-158 (February 2012): 796–99. http://dx.doi.org/10.4028/www.scientific.net/amm.157-158.796.

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In recent years there has been a growing interest in the study of sparse representation of signals. The redundancy of over-complete dictionary can make it effectively capture the characteristics of the signals. Using an over-complete dictionary that contains prototype signal-atoms, signals are described as linear combinations of a few of these atoms. Applications that use sparse representation are many and include compression, regularization in inverse problems, Compressed Sensing (CS), and more. Recent activities in this field concentrate mainly on the study of sparse decomposition algorithm and dictionary design algorithm. In this paper, we discuss the advantages of sparse dictionaries, and present the implicit dictionaries for signal sparse presents. The overcomplete dictionaries which combined the different orthonormal transform bases can be used for the compressed sensing. Experimental results demonstrate the effectivity for sparse presents of signals.

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18

Rubinstein, R., M. Zibulevsky, and M. Elad. "Double Sparsity: Learning Sparse Dictionaries for Sparse Signal Approximation." IEEE Transactions on Signal Processing 58, no. 3 (March 2010): 1553–64. http://dx.doi.org/10.1109/tsp.2009.2036477.

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19

Sun, Tao, Hui Zhang, and Lizhi Cheng. "Subgradient projection for sparse signal recovery with sparse noise." Electronics Letters 50, no. 17 (August 2014): 1200–1202. http://dx.doi.org/10.1049/el.2014.1335.

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20

Hu, Nan, Zhongfu Ye, Xu Xu, and Ming Bao. "DOA Estimation for Sparse Array via Sparse Signal Reconstruction." IEEE Transactions on Aerospace and Electronic Systems 49, no. 2 (April 2013): 760–73. http://dx.doi.org/10.1109/taes.2013.6494379.

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21

Stanković, Ljubiša, and Miloš Daković. "On the Uniqueness of the Sparse Signals Reconstruction Based on the Missing Samples Variation Analysis." Mathematical Problems in Engineering 2015 (2015): 1–14. http://dx.doi.org/10.1155/2015/629759.

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An approach to sparse signals reconstruction considering its missing measurements/samples as variables is recently proposed. Number and positions of missing samples determine the uniqueness of the solution. It has been assumed that analyzed signals are sparse in the discrete Fourier transform (DFT) domain. A theorem for simple uniqueness check is proposed. Two forms of the theorem are presented, for an arbitrary sparse signal and for an already reconstructed signal. The results are demonstrated on illustrative and statistical examples.

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22

Plonka, Gerlind, Kilian Stampfer, and Ingeborg Keller. "Reconstruction of stationary and non-stationary signals by the generalized Prony method." Analysis and Applications 17, no. 02 (March 2019): 179–210. http://dx.doi.org/10.1142/s0219530518500240.

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We employ the generalized Prony method in [T. Peter and G. Plonka, A generalized Prony method for reconstruction of sparse sums of eigenfunctions of linear operators, Inverse Problems 29 (2013) 025001] to derive new reconstruction schemes for a variety of sparse signal models using only a small number of signal measurements. By introducing generalized shift operators, we study the recovery of sparse trigonometric and hyperbolic functions as well as sparse expansions into Gaussians chirps and modulated Gaussian windows. Furthermore, we show how to reconstruct sparse polynomial expansions and sparse non-stationary signals with structured phase functions.

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23

Wang, Baoxiang, Yuhe Liao, Rongkai Duan, and Xining Zhang. "Sparse Low-Rank Based Signal Analysis Method for Bearing Fault Feature Extraction." Applied Sciences 10, no. 7 (March 30, 2020): 2358. http://dx.doi.org/10.3390/app10072358.

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The condition monitoring of rolling element bearings (REBs) is essential to maintain the reliable operation of rotating machinery, and the difficulty lies in how to estimate fault information from the raw signal that is always overwhelmed by severe background noise and other interferences. The method based on a sparse model has attracted increasing attention because it can capture deep-level fault features. However, when processing a signal with complex components and weak fault features, the performance of sparse model-based methods is often not ideal. In this work, the fault information-based sparse low-rank algorithm (FISLRA) is proposed to abstract the fault information from a noisy signal interfered with by background noise and external interference. Concretely, a sparse and low-rank model is formulated in the time-frequency domain. Then, a fast-converging algorithm is derived based on the alternating direction method of multipliers (ADMM) to solve the formulated model. Moreover, to further highlight the periodical transients, a correlated kurtosis-based thresholding (CKT) scheme proposed in this paper is also incorporated to solve the proposed low-rank spares model. The superiority of the proposed FISLRA over the traditional sparse low-rank model (TSLRM) and spectral kurtosis (SK) is proved by simulation analysis. In addition, two experimental signals collected from a bearing test rig are utilized to demonstrate the efficiency of the proposed FISLRA in fault detection. The results illustrate that compared to the TSLRM method, FISLRA can effectively extract periodical fault transients even when harmonic components (HCs) are present in the noisy signal.

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24

Stankovic, Ljubisa. "Noises in randomly sampled sparse signals." Facta universitatis - series: Electronics and Energetics 27, no. 3 (2014): 359–73. http://dx.doi.org/10.2298/fuee1403359s.

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Sparse signals can be recovered from a reduced set of randomly positioned samples by using compressive sensing algorithms. Two main reconstruction directions are in the sparse transformation domain analysis of signals and the gradient based algorithms. In the transformation domain analysis, that will be considered here, the estimation of nonzero signal coefficients is based on the signal transform calculated using available samples only. The missing samples manifest themselves as a noise. This kind of noise is analyzed in the case of random sampling, when the sampling instants do not coincide with the sampling theorem instants. Analysis of the external noise influence to the results, with randomly sampled sparse signals, is done as well. Theory is illustrated and checked on statistical examples.

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25

Hou, Thomas Y., and Zuoqiang Shi. "Sparse time-frequency decomposition based on dictionary adaptation." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 374, no. 2065 (April 13, 2016): 20150192. http://dx.doi.org/10.1098/rsta.2015.0192.

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In this paper, we propose a time-frequency analysis method to obtain instantaneous frequencies and the corresponding decomposition by solving an optimization problem. In this optimization problem, the basis that is used to decompose the signal is not known a priori . Instead, it is adapted to the signal and is determined as part of the optimization problem. In this sense, this optimization problem can be seen as a dictionary adaptation problem, in which the dictionary is adaptive to one signal rather than a training set in dictionary learning. This dictionary adaptation problem is solved by using the augmented Lagrangian multiplier (ALM) method iteratively. We further accelerate the ALM method in each iteration by using the fast wavelet transform. We apply our method to decompose several signals, including signals with poor scale separation, signals with outliers and polluted by noise and a real signal. The results show that this method can give accurate recovery of both the instantaneous frequencies and the intrinsic mode functions.

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26

Liang, Shuang, and Lu Li. "Reconstruction of EEG Signal Based on Compressed Sensing and Wavelet Transform." Applied Mechanics and Materials 734 (February 2015): 617–20. http://dx.doi.org/10.4028/www.scientific.net/amm.734.617.

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This paper, both theoretically and numerically, investigates an effective reconstruction of EEG signal. An optimization model is presented, which unifies different sparse signals. The model is solved by employing the proximal algorithm. Based on the theoretical analysis, the simulation of EEG signal is performed. Sparse representation of EEG signal is got by the technique of wavelet transform and the signal denoising is also obtained. Then, by using compressed sensing, the EEG signal is reconstructed. Our results show that the reconstructed signal is in good agreement with the original signal and retains the leading characteristic.

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27

Li, Yong Ting, Xiao Yan Chen, and Yue Wen Liu. "Multi-Channel ECG Signals Compression Algorithm Using Simultaneous Orthogonal Matching Pursuit." Advanced Materials Research 457-458 (January 2012): 1305–9. http://dx.doi.org/10.4028/www.scientific.net/amr.457-458.1305.

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Sparse decompression is a new theory for signal processing, having the advantage in that the base (dictionary) used in this theory is over-complete, and can reflect the nature of signa1. So the sparse decompression of signal can get sparse representation, which is very important in data compression. In this paper, a novel ECG compression method for multi-channel ECG signals was introduced based on the Simultaneous Orthogonal Matching Pursuit (S-OMP). The proposed method decomposes multi-channel ECG signals simultaneously into different linear expansions of the same atoms that are selected from a redundant dictionary, which is constructed by Hermite fuctions and Gobar functions in order to the best match the characteristic of the ECG waveform. Compression performance has been tested using a subset of multi-channel ECG records from the St.-Petersburg Institute of Cardiological Technics database, the results demonstrate that much less atoms are selected to present signals and the compression ratio of Multi-channel ECG can achieve better performance in comparison to Simultaneous Matching Pursuit (SMP).

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Chen, Wengu, and Huanmin Ge. "A Sharp Bound on RIC in Generalized Orthogonal Matching Pursuit." Canadian Mathematical Bulletin 61, no. 1 (March 1, 2018): 40–54. http://dx.doi.org/10.4153/cmb-2017-009-6.

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AbstractThe generalized orthogonal matching pursuit (gOMP) algorithm has received much attention in recent years as a natural extension of the orthogonal matching pursuit (OMP). It is used to recover sparse signals in compressive sensing. In this paper, a new bound is obtained for the exact reconstruction of every K-sparse signal via the gOMP algorithm in the noiseless case. That is, if the restricted isometry constant (RIC) δNK+1 of the sensing matrix A satisfiesthen the gOMP can perfectly recover every K-sparse signal x from y = Ax. Furthermore, the bound is proved to be sharp. In the noisy case, the above bound on RIC combining with an extra condition on the minimum magnitude of the nonzero components of K-sparse signals can guarantee that the gOMP selects all of the support indices of the K-sparse signals.

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Mishra, Ishani, and Sanjay Jain. "Soft computing based compressive sensing techniques in signal processing: A comprehensive review." Journal of Intelligent Systems 30, no. 1 (September 11, 2020): 312–26. http://dx.doi.org/10.1515/jisys-2019-0215.

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Abstract In this modern world, a massive amount of data is processed and broadcasted daily. This includes the use of high energy, massive use of memory space, and increased power use. In a few applications, for example, image processing, signal processing, and possession of data signals, etc., the signals included can be viewed as light in a few spaces. The compressive sensing theory could be an appropriate contender to manage these limitations. “Compressive Sensing theory” preserves extremely helpful while signals are sparse or compressible. It very well may be utilized to recoup light or compressive signals with less estimation than customary strategies. Two issues must be addressed by CS: plan of the estimation framework and advancement of a proficient sparse recovery calculation. The essential intention of this work expects to audit a few ideas and utilizations of compressive sensing and to give an overview of the most significant sparse recovery calculations from every class. The exhibition of acquisition and reconstruction strategies is examined regarding the Compression Ratio, Reconstruction Accuracy, Mean Square Error, and so on.

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Xie, Zhengguang, Hongwei Huang, and Xu Cai. "Matching Pursuit for Sparse Signal Reconstruction Based on Dual Thresholds." International Journal of Computer and Communication Engineering 5, no. 5 (2016): 341–49. http://dx.doi.org/10.17706/ijcce.2016.5.5.341-349.

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31

Khanna, Saurabh, and Chandra R. Murthy. "Decentralized Joint-Sparse Signal Recovery: A Sparse Bayesian Learning Approach." IEEE Transactions on Signal and Information Processing over Networks 3, no. 1 (March 2017): 29–45. http://dx.doi.org/10.1109/tsipn.2016.2612120.

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32

Et.al, Sudha Hanumanthu. "Universal Measurement Matrix Design for Sparse and Co-Sparse Signal Recovery." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 6 (April 10, 2021): 404–11. http://dx.doi.org/10.17762/turcomat.v12i6.1407.

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Compressed Sensing (CS) avails mutual coherence metric to choose the measurement matrix that is incoherent with dictionary matrix. Random measurement matrices are incoherent with any dictionary, but their highly uncertain elements necessitate large storage and make hardware realization difficult. In this paper deterministic matrices are employed which greatly reduce memory space and computational complexity. To avoid the randomness completely, deterministic sub-sampling is done by choosing rows deterministically rather than randomly, so that matrix can be regenerated during reconstruction without storing it. Also matrices are generated by orthonormalization, which makes them highly incoherent with any dictionary basis. Random matrices like Gaussian, Bernoulli, semi-deterministic matrices like Toeplitz, Circulant and full-deterministic matrices like DFT, DCT, FZC-Circulant are compared. DFT matrix is found to be effective in terms of recovery error and recovery time for all the cases of signal sparsity and is applicable for signals that are sparse in any basis, hence universal.

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33

XI, FENG, SHENGYAO CHEN, and ZHONG LIU. "CHAOTIC ANALOG-TO-INFORMATION CONVERSION: PRINCIPLE AND RECONSTRUCTABILITY WITH PARAMETER IDENTIFIABILITY." International Journal of Bifurcation and Chaos 23, no. 12 (December 2013): 1350198. http://dx.doi.org/10.1142/s0218127413501988.

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This paper proposes a chaos-based analog-to-information conversion system for the acquisition and reconstruction of sparse analog signals. The sparse signal acts as an excitation term of a continuous-time chaotic system and the compressive measurements are performed by sampling chaotic system outputs. The reconstruction is realized through the estimation of the sparse coefficients by the principle of chaotic parameter estimation. With the deterministic formulation, the analysis on the reconstructability is conducted via the sensitivity matrix from the parameter identifiability of chaotic systems. For the sparsity-regularized nonlinear least squares estimation, it is shown that the sparse signal is locally reconstructable if the columns of the sparsity-regularized sensitivity matrix are linearly independent. A Lorenz system excited by the sparse multitone signal is taken as an example to illustrate the principle and the performance.

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Wang, Jing Hui, and Shu Gang Tang. "Quadratic Independent Component Analysis Based on Sparse Component." Applied Mechanics and Materials 442 (October 2013): 562–67. http://dx.doi.org/10.4028/www.scientific.net/amm.442.562.

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In this paper, a novel signal blind separation using adaptive multi-resolution independent component analysis based on sparse component is presented. This method separates mixed signal based on quadratic function and sparse representation. The quadratic function can be interpreted as the time-frequency function or time-scale function, or other. The sparse expression is the original signal through the dictionary to get their coefficients. Most of the coefficients is very small, close to zero, can greatly save separate computing time. At the same time this method can filter out the noise. The argorithm extends the separate technology from time-frequency domain to sparse mutil-resolution domain. The experimental result showed the method can be effective separation of mixed signals. And it shows that the method is feasible.

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Zhang, Anan, Cong He, Maoyi Sun, Qian Li, Hong Wei Li, and Lin Yang. "Partial discharge signal self-adaptive sparse decomposition noise abatement based on spectral kurtosis and S-transform." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 37, no. 1 (January 2, 2018): 293–306. http://dx.doi.org/10.1108/compel-03-2017-0126.

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Purpose Noise abatement is one of the key techniques for Partial Discharge (PD) on-line measurement and monitoring. However, how to enhance the efficiency of PD signal noise suppression is a challenging work. Hence, this study aims to improve the efficiency of PD signal noise abatement. Design/methodology/approach In this approach, the time–frequency characteristics of PD signal had been obtained based on fast kurtogram and S-transform time–frequency spectrum, and these characteristics were used to optimize the parameters for the signal matching over-complete dictionary. Subsequently, a self-adaptive selection of matching atoms was realized when using Matching Pursuit (MP) to analyze PD signals, which leading to seldom noise signal element was represented in sparse decomposition. Findings The de-noising of PD signals was achieved efficiently. Simulation and experimental results show that the proposed method has good adaptability and significant noise abatement effect compared with Empirical Mode Decomposition, Wavelet Threshold and global signal sparse decomposition of MP. Originality/value A self-adaptive noise abatement method was proposed to improve the efficiency of PD signal noise suppression based on the signal sparse representation and its MP algorithm, which is significant to on-line PD measurement.

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Zhao, Hongbo, Lei Chen, Wenquan Feng, and Chuan Lei. "A Novel Detection Scheme with Multiple Observations for Sparse Signal Based on Likelihood Ratio Test with Sparse Estimation." Mathematical Problems in Engineering 2016 (2016): 1–14. http://dx.doi.org/10.1155/2016/8535486.

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Recently, the problem of detecting unknown and arbitrary sparse signals has attracted much attention from researchers in various fields. However, there remains a peck of difficulties and challenges as the key information is only contained in a small fraction of the signal and due to the absence of prior information. In this paper, we consider a more general and practical scenario of multiple observations with no prior information except for the sparsity of the signal. A new detection scheme referred to as the likelihood ratio test with sparse estimation (LRT-SE) is presented. Under the Neyman-Pearson testing framework, LRT-SE estimates the unknown signal by employing thel1-minimization technique from compressive sensing theory. The detection performance of LRT-SE is preliminarily analyzed in terms of error probabilities in finite size and Chernoff consistency in high dimensional condition. The error exponent is introduced to describe the decay rate of the error probability as observations number grows. Finally, these properties of LRT-SE are demonstrated based on the experimental results of synthetic sparse signals and sparse signals from real satellite telemetry data. It could be concluded that the proposed detection scheme performs very close to the optimal detector.

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Chen, Xu, Guoyu Lin, and Yuxin Zhang. "Denoising Method Based on Sparse Representation for WFT Signal." Journal of Sensors 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/145870.

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Affected by external noise and various nature disturbances, Wheel Force Transducer (WFT) signal may be completely submerged, and the sensitivity and the reliability of measurement can be strongly decreased. In this paper, a new wavelet packet denoising method based on sparse representation is proposed to remove the noises from WFT signal. In this method, the problem of recovering the noiseless signal is converted into an optimization problem of recovering the sparsity of their wavelet package coefficients, and the wavelet package coefficients of the noiseless signals can be obtained by the augmented Lagrange optimization method. Then the denoised WFT signal can be reconstructed by wavelet packet reconstruction. The experiments on simulation signal and WFT signal show that the proposed denoising method based on sparse representation is more effective for denoising WFT signal than the soft and hard threshold denoising methods.

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Kennett, B. L. N. "Signal Parameter Estimation for Sparse Arrays." Bulletin of the Seismological Society of America 93, no. 4 (August 1, 2003): 1765–72. http://dx.doi.org/10.1785/0120020221.

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Hu, Xiao-Li, Jiajun Wen, Wai Keung Wong, Le Tong, and Jinrong Cui. "On uniqueness of sparse signal recovery." Signal Processing 150 (September 2018): 66–74. http://dx.doi.org/10.1016/j.sigpro.2018.04.002.

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Selesnick, Ivan, and Masoud Farshchian. "Sparse Signal Approximation via Nonseparable Regularization." IEEE Transactions on Signal Processing 65, no. 10 (May 15, 2017): 2561–75. http://dx.doi.org/10.1109/tsp.2017.2669904.

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Ito, Daisuke, Satoshi Takabe, and Tadashi Wadayama. "Trainable ISTA for Sparse Signal Recovery." IEEE Transactions on Signal Processing 67, no. 12 (June 15, 2019): 3113–25. http://dx.doi.org/10.1109/tsp.2019.2912879.

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Şahin, Ahmet, and Serdar Özen. "Constraint removal for sparse signal recovery." Signal Processing 92, no. 4 (April 2012): 1172–75. http://dx.doi.org/10.1016/j.sigpro.2011.11.014.

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Zhang, Li, Wei-Da Zhou, Gui-Rong Chen, Ya-Ping Lu, and Fan-Zhang Li. "Sparse signal reconstruction using decomposition algorithm." Knowledge-Based Systems 54 (December 2013): 172–79. http://dx.doi.org/10.1016/j.knosys.2013.09.007.

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Aase, S. O., J. H. Husoy, J. H. H. K. Skretting, and K. Engan. "Optimized signal expansions for sparse representation." IEEE Transactions on Signal Processing 49, no. 5 (May 2001): 1087–96. http://dx.doi.org/10.1109/78.917811.

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Erkoc, Murat Emre, and Nurhan Karaboga. "Evolutionary algorithms for sparse signal reconstruction." Signal, Image and Video Processing 13, no. 7 (April 16, 2019): 1293–301. http://dx.doi.org/10.1007/s11760-019-01473-w.

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Bayisa, Fekadu L., Zhiyong Zhou, Ottmar Cronie, and Jun Yu. "Adaptive algorithm for sparse signal recovery." Digital Signal Processing 87 (April 2019): 10–18. http://dx.doi.org/10.1016/j.dsp.2019.01.002.

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Liou, Ren Jean. "Ultrasonic Signal Reconstruction Using Compressed Sensing." Applied Mechanics and Materials 855 (October 2016): 165–70. http://dx.doi.org/10.4028/www.scientific.net/amm.855.165.

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Ultrasonic signal reconstruction for Structural Health Monitoring is a topic that has been discussed extensively. In this paper, we will apply the techniques of compressed sensing to reconstruct ultrasonic signals that are seriously damaged. To reconstruct the data, the application of conventional interpolation techniques is restricted under the criteria of Nyquist sampling theorem. The newly developed technique - compressed sensing breaks the limitations of Nyquist rate and provides effective results based upon sparse signal reconstruction. Sparse representation is constructed using Fourier transform basis. An l1-norm optimization is then applied for reconstruction. Signals with temperature characteristics were synthetically created. We seriously corrupted these signals and tested the efficacy of our approach under two different scenarios. Firstly, the signal is randomly sampled at very low rates. Secondly, selected intervals were completely blank out. Simulation results show that the signals are effectively reconstructed. It outperforms conventional Spline interpolation in signal-to-noise ratio (SNR) with low variation, especially under very low data rates. This research demonstrates very promising results of using compressed sensing for ultrasonic signal reconstruction.

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Andrysiak, Tomasz, and Łukasz Saganowski. "Anomaly detection system based on sparse signal representation." Image Processing & Communications 16, no. 3-4 (January 1, 2011): 37–44. http://dx.doi.org/10.2478/v10248-012-0010-6.

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Anomaly detection system based on sparse signal representationIn this paper we present further expansion of our matching pursuit methodology for anomaly detection in computer networks. In our previous work we proposed new signal based algorithm for intrusion detection systems based on anomaly detection approach on the basis of the Matching Pursuit algorithm. This time we present completely different approach to generating base functions (atoms) dictionary. We propose modification of K-SVD [1] algorithm in order to select atoms from real 1-D signal which represents network traffic features. Dictionary atoms selected in this way have the ability to approximate different 1-D signals representing network traffic features. Achieved dictionary was used to detect network anomalies on benchmark data sets. Results were compared to the dictionary based on analytical 1-D Gabor atoms.

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Dziwoki, Grzegorz, and Marcin Kucharczyk. "On a Sparse Approximation of Compressible Signals." Circuits, Systems, and Signal Processing 39, no. 4 (October 18, 2019): 2232–43. http://dx.doi.org/10.1007/s00034-019-01287-8.

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Abstract Many physical phenomena can be modeled by compressible signals, i.e., the signals with rapidly declining sample amplitudes. Although all the samples are usually nonzero, due to practical reasons such signals are attempted to be approximated as sparse ones. Because sparsity of compressible signals cannot be unambiguously determined, a decision about a particular sparse representation is often a result of comparison between a residual error energy of a reconstruction algorithm and some quality measure. The paper explores a relation between mean square error (MSE) of the recovered signal and the residual error. A novel, practical solution that controls the sparse approximation quality using a target MSE value is the result of these considerations. The solution was tested in numerical experiments using orthogonal matching pursuit (OMP) algorithm as the signal reconstruction procedure. The obtained results show that the proposed quality metric provides fine control over the approximation process of the compressible signals in the mean sense even though it has not been directly designed for use in compressed sensing methods such as OMP.

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Khalandar Basha, D., and T. Venkateswarlu. "Algorithms on Sparse Representation." International Journal of Engineering & Technology 7, no. 4.36 (December 9, 2018): 569. http://dx.doi.org/10.14419/ijet.v7i4.36.24139.

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Representation of signals and images in sparse become more interesting for various applications like restoration, compression and recognition. Many researches carried out in the era of sparse representation. Sparse represents signal or image as a few elements from the dictionary atoms. There are various algorithms proposed by researchers for learning dictionary. This paper discuss some of the terms related to sparse like regularization term, minimization, minimization, minimizationfollowed by the pursuit algorithms for solving problem, greedy algorithms and relaxation algorithms. This paper gives algorithmic approaches for the algorithms.

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