In this paper,we reconstruct strongly-decaying block sparse signals by the block generalized orthogonal matching pursuit(BgOMP)algorithm in the l2-bounded noise case.Under some restraints on the minimum magnitude of t...In this paper,we reconstruct strongly-decaying block sparse signals by the block generalized orthogonal matching pursuit(BgOMP)algorithm in the l2-bounded noise case.Under some restraints on the minimum magnitude of the nonzero elements of the strongly-decaying block sparse signal,if the sensing matrix satisfies the the block restricted isometry property(block-RIP),then arbitrary strongly-decaying block sparse signals can be accurately and steadily reconstructed by the BgOMP algorithm in iterations.Furthermore,we conjecture that this condition is sharp.展开更多
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 o...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.展开更多
Sparse signal is a kind of sparse matrices which can carry fault information and simplify the signal at the same time.This can effectively reduce the cost of signal storage,improve the efficiency of data transmission,...Sparse signal is a kind of sparse matrices which can carry fault information and simplify the signal at the same time.This can effectively reduce the cost of signal storage,improve the efficiency of data transmission,and ultimately save the cost of equipment fault diagnosis in the aviation field.At present,the existing sparse decomposition methods generally extract sparse fault characteristics signals based on orthogonal basis atoms,which limits the adaptability of sparse decomposition.In this paper,a self-adaptive atom is extracted by the improved dual-channel tunable Q-factor wavelet transform(TQWT)method to construct a self-adaptive complete dictionary.Finally,the sparse signal is obtained by the orthogonal matching pursuit(OMP)algorithm.The atoms obtained by this method are more flexible,and are no longer constrained to an orthogonal basis to reflect the oscillation characteristics of signals.Therefore,the sparse signal can better extract the fault characteristics.The simulation and experimental results show that the selfadaptive dictionary with the atom extracted from the dual-channel TQWT has a stronger decomposition freedom and signal matching ability than orthogonal basis dictionaries,such as discrete cosine transform(DCT),discrete Hartley transform(DHT)and discrete wavelet transform(DWT).In addition,the sparse signal extracted by the self-adaptive complete dictionary can reflect the time-domain characteristics of the vibration signals,and can more accurately extract the bearing fault feature frequency.展开更多
The detection of sparse signals against background noise is considered. Detecting signals of such kind is difficult since only a small portion of the signal carries information. Prior knowledge is usually assumed to e...The detection of sparse signals against background noise is considered. Detecting signals of such kind is difficult since only a small portion of the signal carries information. Prior knowledge is usually assumed to ease detection. In this paper, we consider the general unknown and arbitrary sparse signal detection problem when no prior knowledge is available. Under a Ney- man-Pearson hypothesis-testing framework, a new detection scheme is proposed by combining a generalized likelihood ratio test （GLRT）-Iike test statistic and convex programming methods which directly exploit sparsity in an underdetermined system of linear equations. We characterize large sample behavior of the proposed method by analyzing its asymptotic performance. Specifically, we give the condition for the Chernoff-consistent detection which shows that the proposed method is very sensitive to the norm energy of the sparse signals. Both the false alam rate and the miss rate tend to zero at vanishing signal-to-noise ratio （SNR）, as long as the signal energy grows at least logarithmically with the problem dimension. Next we give a large deviation analysis to characterize the error exponent for the Neyman-Pearson detection. We derive the oracle error exponent assuming signal knowledge. Then we explicitly derive the error exponent of the proposed scheme and compare it with the oracle exponent. We complement our study with numerical experiments, showing that the proposed method performs in the vicinity of the likelihood ratio test （LRT） method in the finite sample scenario and the error probability degrades exponentially with the number of observations.展开更多
Sparse signal recovery is a topic of considerable interest,and the literature in this field is already quite immense.Many problems that arise in sparse signal recovery can be generalized as a convex programming with l...Sparse signal recovery is a topic of considerable interest,and the literature in this field is already quite immense.Many problems that arise in sparse signal recovery can be generalized as a convex programming with linear conic constraints.In this paper,we present a new proximal point algorithm(PPA) termed as relaxed-PPA(RPPA) contraction method,for solving this common convex programming.More precisely,we first reformulate the convex programming into an equivalent variational inequality(VI),and then efficiently explore its inner structure.In each step,our method relaxes the VI-subproblem to a tractable one,which can be solved much more efficiently than the original VI.Under mild conditions,the convergence of the proposed method is proved.Experiments with l1 analysis show that RPPA is a computationally efficient algorithm and compares favorably with the recently proposed state-of-the-art algorithms.展开更多
A fundamental problem in some applications including group testing and communications is to acquire the support of a K-sparse signal x,whose nonzero elements are 1,from an underdetermined noisy linear model.This paper...A fundamental problem in some applications including group testing and communications is to acquire the support of a K-sparse signal x,whose nonzero elements are 1,from an underdetermined noisy linear model.This paper first designs an algorithm called binary least squares(BLS)to reconstruct x and analyzes its complexity.Then,we establish two sufficient conditions for the exact reconstruction of x’s support with K iterations of BLS based on the mutual coherence and restricted isometry property of the measurement matrix,respectively.Finally,extensive numerical tests are performed to compare the efficiency and effectiveness of BLS with those of batch orthogonal matching pursuit(BatchOMP)which to our best knowledge is the fastest implementation of OMP,orthogonal least squares(OLS),compressive sampling matching pursuit(CoSaMP),hard thresholding pursuit(HTP),Newton-step-based iterative hard thresholding(NSIHT),Newton-step-based hard thresholding pursuit(NSHTP),binary matching pursuit(BMP)andΙ_(1)-regularized least squares.Test results show that:(1)BLS can be 10-200 times more efficient than Batch-OMP,OLS,CoSaMP,HTP,NSIHT and NSHTP with higher probability of support reconstruction,and the improvement can be 20%-80%;(2)BLS has more than 25%improvement on the support reconstruction probability than the explicit BMP algorithm with a little higher computational complexity;(3)BLS is around 100 times faster thanΙ_(1)regularized least squares with lower support reconstruction probability for small K and higher support reconstruction probability for large K.Numerical tests on the generalized space shift keying(GSSK)detection indicate that although BLS is a little slower than BMP,it is more efficient than the other seven tested sparse recovery algorithms,and although it is less effective thanΙ_(1)-regularized least squares,it is more effective than the other seven algorithms.展开更多
Sparse signal processing is a signal processing technique that takes advantage of signal’s sparsity,allowing signal to be recovered with a reduced number of samples.Compressive sensing,a new branch of the sparse sign...Sparse signal processing is a signal processing technique that takes advantage of signal’s sparsity,allowing signal to be recovered with a reduced number of samples.Compressive sensing,a new branch of the sparse signal processing,has become a rapidly growing research field.Sparse microwave imaging introduces the sparse signal processing theory to radar imaging to obtain new theories,new systems and new methodologies of microwave imaging.This paper first summarizes the latest application of sparse microwave imaging,including Synthetic Aperture Radar(SAR),tomographic SAR and inverse SAR.As sparse signal processing keeps evolving,an avalanche of results have been obtained.We also highlight its recent theoretical advances,including structured sparsity,off-grid,Bayesian approaches,and point out new research directions in sparse microwave imaging.展开更多
We consider the block orthogonal multi-matching pursuit(BOMMP) algorithm for the recovery of block sparse signals.A sharp condition is obtained for the exact reconstruction of block K-sparse signals via the BOMMP algo...We consider the block orthogonal multi-matching pursuit(BOMMP) algorithm for the recovery of block sparse signals.A sharp condition is obtained for the exact reconstruction of block K-sparse signals via the BOMMP algorithm in the noiseless case,based on the block restricted isometry constant(block-RIC).Moreover,we show that the sharp condition combining with an extra condition on the minimum l_2 norm of nonzero blocks of block K-sparse signals is sufficient to ensure the BOMMP algorithm selects at least one true block index at each iteration until all true block indices are selected in the noisy case.The significance of the results we obtain in this paper lies in the fact that making explicit use of block sparsity of block sparse signals can achieve better recovery performance than ignoring the additional structure in the problem as being in the conventional sense.展开更多
A direction-of-arrival （DOA） estimation algorithm is presented based on covariance differencing and sparse signal recovery, in which the desired signal is embedded in noise with unknown covariance. The key point of ...A direction-of-arrival （DOA） estimation algorithm is presented based on covariance differencing and sparse signal recovery, in which the desired signal is embedded in noise with unknown covariance. The key point of the algorithm is to eliminate the noise component by forming the difference of original and transformed covariance matrix, as well as cast the DOA estimation considered as a sparse signal recovery problem. Concerning accuracy and complexity of estimation, the authors take a vectorization operation on difference matrix, and further enforce sparsity by reweighted l1-norm penalty. We utilize data-validation to select the regularization parameter properly. Meanwhile, a kind of symmetric grid division and refinement strategy is introduced to make the proposed algorithm effective and also to mitigate the effects of limiting estimates to a grid of spatial locations. Compared with the covariance-differencing-based multiple signal classification （MUSIC） method, the proposed is of salient features, including increased resolution, improved robustness to colored noise, distinguishing the false peaks easily, but with no requiring of prior knowledge of the number of sources.展开更多
Distributed compressed sensing （DCS） is an emerging research field which exploits both intra-signal and inter-signal correlations. This paper focuses on the recovery of the sparse signals which can be modeled as joi...Distributed compressed sensing （DCS） is an emerging research field which exploits both intra-signal and inter-signal correlations. This paper focuses on the recovery of the sparse signals which can be modeled as joint sparsity model （JSM） 2 with different nonzero coefficients in the same location set. Smoothed L0 norm algorithm is utilized to convert a non-convex and intractable mixed L2,0 norm optimization problem into a solvable one. Compared with a series of single-measurement-vector problems, the proposed approach can obtain a better reconstruction performance by exploiting the inter-signal correlations. Simulation results show that our algorithm outperforms L1,1 norm optimization for both noiseless and noisy cases and is more robust against thermal noise compared with LI,2 recovery. Besides, with the help of the core concept of modified compressed sensing （CS） that utilizes partial known support as side information, we also extend this algorithm to decode correlated row sparse signals generated following JSM 1.展开更多
This paper aims to investigate sufficient conditions for the recovery of sparse signals via the orthogonal matching pursuit （OMP） algorithm. In the noiseless case, we present a novel sufficient condition for the exa...This paper aims to investigate sufficient conditions for the recovery of sparse signals via the orthogonal matching pursuit （OMP） algorithm. In the noiseless case, we present a novel sufficient condition for the exact recovery of all k-sparse signals by the OMP algorithm, and demonstrate that this condition is sharp. In the noisy case, a sufficient condition for recovering the support of k-sparse signal is also presented. Generally, the computation for the restricted isometry constant （RIC） in these sufficient conditions is typically difficult, therefore we provide a new condition which is not only computable but also sufficient for the exact recovery of all k-sparse signals.展开更多
In countless applications,we need to reconstruct a K-sparse signal x∈R n from noisy measurements y=Φx+v,whereΦ∈R^(m×n)is a sensing matrix and v∈R m is a noise vector.Orthogonal least squares(OLS),which selec...In countless applications,we need to reconstruct a K-sparse signal x∈R n from noisy measurements y=Φx+v,whereΦ∈R^(m×n)is a sensing matrix and v∈R m is a noise vector.Orthogonal least squares(OLS),which selects at each step the column that results in the most significant decrease in the residual power,is one of the most popular sparse recovery algorithms.In this paper,we investigate the number of iterations required for recovering x with the OLS algorithm.We show that OLS provides a stable reconstruction of all K-sparse signals x in[2.8K]iterations provided thatΦsatisfies the restricted isometry property(RIP).Our result provides a better recovery bound and fewer number of required iterations than those proposed by Foucart in 2013.展开更多
Pulse signal recovery is to extract useful amplitude and time information from the pulse signal contaminated by noise. It is a great challenge to precisely recover the pulse signal in loud background noise. The conven...Pulse signal recovery is to extract useful amplitude and time information from the pulse signal contaminated by noise. It is a great challenge to precisely recover the pulse signal in loud background noise. The conventional approaches,which are mostly based on the distribution of the pulse energy spectrum,do not well determine the locations and shapes of the pulses. In this paper,we propose a time domain method to reconstruct pulse signals. In the proposed approach,a sparse representation model is established to deal with the issue of the pulse signal recovery under noise conditions. The corresponding problem based on the sparse optimization model is solved by a matching pursuit algorithm. Simulations and experiments validate the effectiveness of the proposed approach on pulse signal recovery.展开更多
For the direction of arrival（DOA） estimation,traditional sparse reconstruction methods for wideband signals usually need many iteration times.For this problem,a new method for two-dimensional wideband signals based ...For the direction of arrival（DOA） estimation,traditional sparse reconstruction methods for wideband signals usually need many iteration times.For this problem,a new method for two-dimensional wideband signals based on block sparse reconstruction is proposed.First,a prolate spheroidal wave function（PSWF） is used to fit the wideband signals,then the block sparse reconstruction technology is employed for DOA estimation.The proposed method uses orthogonalization to choose the matching atoms,ensuring that the residual components correspond to the minimum absolute value.Meanwhile,the vectors obtained by iteration are back-disposed according to the corresponding atomic matching rules,so the extra atoms are abandoned in the course of iteration,and the residual components of current iteration are reduced.Thus the original sparse signals are reconstructed.The proposed method reduces iteration times comparing with the traditional reconstruction methods,and the estimation precision is better than the classical two-sided correlation transformation（TCT）algorithm when the snapshot is small or the signal-to-noise ratio（SNR） is low.展开更多
In many practical applications,we need to recover block sparse signals.In this paper,we encounter the system model where joint sparse signals exhibit block structure.To reconstruct this category of signals,we propose ...In many practical applications,we need to recover block sparse signals.In this paper,we encounter the system model where joint sparse signals exhibit block structure.To reconstruct this category of signals,we propose a new algorithm called block signal subspace matching pursuit(BSSMP)for the block joint sparse recovery problem in compressed sensing,which simultaneously reconstructs the support of block jointly sparse signals from a common sensing matrix.To begin with,we consider the case where block joint sparse matrix X has full column rank and any r nonzero rowblocks are linearly independent.Based on these assumptions,our theoretical analysis indicates that the BSSMP algorithm could reconstruct the support of X through at most K-r+[r/L]iterations if sensing matrix A satisfies the block restricted isometry property of order L(K-r)+r+1 with δB_(L(K-r)+r+1)<max{√r/√K+r/4+√r/4,√L/√Kd+√L}.This condition improves the existing result.展开更多
In underdetermined blind source separation, more sources are to be estimated from less observed mixtures without knowing source signals and the mixing matrix. This paper presents a robust clustering algorithm for unde...In underdetermined blind source separation, more sources are to be estimated from less observed mixtures without knowing source signals and the mixing matrix. This paper presents a robust clustering algorithm for underdetermined blind separation of sparse sources with unknown number of sources in the presence of noise. It uses the robust competitive agglomeration （RCA） algorithm to estimate the source number and the mixing matrix, and the source signals then are recovered by using the interior point linear programming. Simulation results show good performance of the proposed algorithm for underdetermined blind sources separation （UBSS）.展开更多
It is understood that the sparse signal recovery with a standard compressive sensing（CS） strategy requires the measurement matrix known as a priori. The measurement matrix is, however, often perturbed in a practical...It is understood that the sparse signal recovery with a standard compressive sensing（CS） strategy requires the measurement matrix known as a priori. The measurement matrix is, however, often perturbed in a practical application.In order to handle such a case, an optimization problem by exploiting the sparsity characteristics of both the perturbations and signals is formulated. An algorithm named as the sparse perturbation signal recovery algorithm（SPSRA） is then proposed to solve the formulated optimization problem. The analytical results show that our SPSRA can simultaneously recover the signal and perturbation vectors by an alternative iteration way, while the convergence of the SPSRA is also analytically given and guaranteed. Moreover, the support patterns of the sparse signal and structured perturbation shown are the same and can be exploited to improve the estimation accuracy and reduce the computation complexity of the algorithm. The numerical simulation results verify the effectiveness of analytical ones.展开更多
A greedy algorithm used for the recovery of sparse signals,multiple orthogonal least squares(MOLS)have recently attracted quite a big of attention.In this paper,we consider the number of iterations required for the MO...A greedy algorithm used for the recovery of sparse signals,multiple orthogonal least squares(MOLS)have recently attracted quite a big of attention.In this paper,we consider the number of iterations required for the MOLS algorithm for recovery of a K-sparse signal x∈R^(n).We show that MOLS provides stable reconstruction of all K-sparse signals x from y=Ax+w in|6K/ M|iterations when the matrix A satisfies the restricted isometry property(RIP)with isometry constantδ_(7K)≤0.094.Compared with the existing results,our sufficient condition is not related to the sparsity level K.展开更多
In this paper,we focus on the recovery of piecewise sparse signals containing both fast-decaying and slow-decaying nonzero entries.In order to improve the performance of classic Orthogonal Matching Pursuit(OMP)and Gen...In this paper,we focus on the recovery of piecewise sparse signals containing both fast-decaying and slow-decaying nonzero entries.In order to improve the performance of classic Orthogonal Matching Pursuit(OMP)and Generalized Orthogonal Matching Pursuit(GOMP)algorithms for solving this problem,we propose the Piecewise Generalized Orthogonal Matching Pursuit(PGOMP)algorithm,by considering the mixed-decaying sparse signals as piecewise sparse signals with two components containing nonzero entries with different decay factors.The algorithm incorporates piecewise selection and deletion to retain the most significant entries according to the sparsity of each component.We provide a theoretical analysis based on the mutual coherence of the measurement matrix and the decay factors of the nonzero entries,establishing a sufficient condition for the PGOMP algorithm to select at least two correct indices in each iteration.Numerical simulations and an image decomposition experiment demonstrate that the proposed algorithm significantly improves the support recovery probability by effectively matching piecewise sparsity with decay factors.展开更多
We consider the problem of constructing one sparse signal from a few measurements. This problem has been extensively addressed in the literature, providing many sub-optimal methods that assure convergence to a locally...We consider the problem of constructing one sparse signal from a few measurements. This problem has been extensively addressed in the literature, providing many sub-optimal methods that assure convergence to a locally optimal solution under specific conditions. There are a few measurements associated with every signal, where the size of each measurement vector is less than the sparse signal＇s size. All of the sparse signals have the same unknown support. We generalize an existing algorithm for the recovery of one sparse signal from a single measurement to this problem and analyze its performances through simulations. We also compare the construction performance with other existing algorithms. Finally, the proposed method also shows advantages over the OMP （Orthogonal Matching Pursuit） algorithm in terms of the computational complexity.展开更多
基金supported by Natural Science Foundation of China(62071262)the K.C.Wong Magna Fund at Ningbo University.
文摘In this paper,we reconstruct strongly-decaying block sparse signals by the block generalized orthogonal matching pursuit(BgOMP)algorithm in the l2-bounded noise case.Under some restraints on the minimum magnitude of the nonzero elements of the strongly-decaying block sparse signal,if the sensing matrix satisfies the the block restricted isometry property(block-RIP),then arbitrary strongly-decaying block sparse signals can be accurately and steadily reconstructed by the BgOMP algorithm in iterations.Furthermore,we conjecture that this condition is sharp.
基金supported by National Natural Science Foundation of China (Grant No. 71271078)National Hi-tech Research and Development Program of China (863 Program, Grant No. 2009AA04Z414)Integration of Industry, Education and Research of Guangdong Province, and Ministry of Education of China (Grant No. 2009B090300312)
文摘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.
基金This work was supported by the National Key R&D Program of China(Grant No.2018YFB1503103).
文摘Sparse signal is a kind of sparse matrices which can carry fault information and simplify the signal at the same time.This can effectively reduce the cost of signal storage,improve the efficiency of data transmission,and ultimately save the cost of equipment fault diagnosis in the aviation field.At present,the existing sparse decomposition methods generally extract sparse fault characteristics signals based on orthogonal basis atoms,which limits the adaptability of sparse decomposition.In this paper,a self-adaptive atom is extracted by the improved dual-channel tunable Q-factor wavelet transform(TQWT)method to construct a self-adaptive complete dictionary.Finally,the sparse signal is obtained by the orthogonal matching pursuit(OMP)algorithm.The atoms obtained by this method are more flexible,and are no longer constrained to an orthogonal basis to reflect the oscillation characteristics of signals.Therefore,the sparse signal can better extract the fault characteristics.The simulation and experimental results show that the selfadaptive dictionary with the atom extracted from the dual-channel TQWT has a stronger decomposition freedom and signal matching ability than orthogonal basis dictionaries,such as discrete cosine transform(DCT),discrete Hartley transform(DHT)and discrete wavelet transform(DWT).In addition,the sparse signal extracted by the self-adaptive complete dictionary can reflect the time-domain characteristics of the vibration signals,and can more accurately extract the bearing fault feature frequency.
基金National Basic Research Program of China(2011CB707000)Innovative Research Group National Natural Science Foundation of China(60921001)
文摘The detection of sparse signals against background noise is considered. Detecting signals of such kind is difficult since only a small portion of the signal carries information. Prior knowledge is usually assumed to ease detection. In this paper, we consider the general unknown and arbitrary sparse signal detection problem when no prior knowledge is available. Under a Ney- man-Pearson hypothesis-testing framework, a new detection scheme is proposed by combining a generalized likelihood ratio test （GLRT）-Iike test statistic and convex programming methods which directly exploit sparsity in an underdetermined system of linear equations. We characterize large sample behavior of the proposed method by analyzing its asymptotic performance. Specifically, we give the condition for the Chernoff-consistent detection which shows that the proposed method is very sensitive to the norm energy of the sparse signals. Both the false alam rate and the miss rate tend to zero at vanishing signal-to-noise ratio （SNR）, as long as the signal energy grows at least logarithmically with the problem dimension. Next we give a large deviation analysis to characterize the error exponent for the Neyman-Pearson detection. We derive the oracle error exponent assuming signal knowledge. Then we explicitly derive the error exponent of the proposed scheme and compare it with the oracle exponent. We complement our study with numerical experiments, showing that the proposed method performs in the vicinity of the likelihood ratio test （LRT） method in the finite sample scenario and the error probability degrades exponentially with the number of observations.
基金the National Natural Science Foundation of China(No.70901018)
文摘Sparse signal recovery is a topic of considerable interest,and the literature in this field is already quite immense.Many problems that arise in sparse signal recovery can be generalized as a convex programming with linear conic constraints.In this paper,we present a new proximal point algorithm(PPA) termed as relaxed-PPA(RPPA) contraction method,for solving this common convex programming.More precisely,we first reformulate the convex programming into an equivalent variational inequality(VI),and then efficiently explore its inner structure.In each step,our method relaxes the VI-subproblem to a tractable one,which can be solved much more efficiently than the original VI.Under mild conditions,the convergence of the proposed method is proved.Experiments with l1 analysis show that RPPA is a computationally efficient algorithm and compares favorably with the recently proposed state-of-the-art algorithms.
基金supported by the NSFC(Grant Nos.12271215,12326378 and 11871248)by the Guangdong Basic and Applied Basic Research Foundation(Grant No.2022A1515010029)by the Guangzhou Science and Technology Foundation Committee(Grant No.202201011126).
文摘A fundamental problem in some applications including group testing and communications is to acquire the support of a K-sparse signal x,whose nonzero elements are 1,from an underdetermined noisy linear model.This paper first designs an algorithm called binary least squares(BLS)to reconstruct x and analyzes its complexity.Then,we establish two sufficient conditions for the exact reconstruction of x’s support with K iterations of BLS based on the mutual coherence and restricted isometry property of the measurement matrix,respectively.Finally,extensive numerical tests are performed to compare the efficiency and effectiveness of BLS with those of batch orthogonal matching pursuit(BatchOMP)which to our best knowledge is the fastest implementation of OMP,orthogonal least squares(OLS),compressive sampling matching pursuit(CoSaMP),hard thresholding pursuit(HTP),Newton-step-based iterative hard thresholding(NSIHT),Newton-step-based hard thresholding pursuit(NSHTP),binary matching pursuit(BMP)andΙ_(1)-regularized least squares.Test results show that:(1)BLS can be 10-200 times more efficient than Batch-OMP,OLS,CoSaMP,HTP,NSIHT and NSHTP with higher probability of support reconstruction,and the improvement can be 20%-80%;(2)BLS has more than 25%improvement on the support reconstruction probability than the explicit BMP algorithm with a little higher computational complexity;(3)BLS is around 100 times faster thanΙ_(1)regularized least squares with lower support reconstruction probability for small K and higher support reconstruction probability for large K.Numerical tests on the generalized space shift keying(GSSK)detection indicate that although BLS is a little slower than BMP,it is more efficient than the other seven tested sparse recovery algorithms,and although it is less effective thanΙ_(1)-regularized least squares,it is more effective than the other seven algorithms.
基金supported by the National Basic Research Program of China("973" Project)(Grant No.2010CB731900)
文摘Sparse signal processing is a signal processing technique that takes advantage of signal’s sparsity,allowing signal to be recovered with a reduced number of samples.Compressive sensing,a new branch of the sparse signal processing,has become a rapidly growing research field.Sparse microwave imaging introduces the sparse signal processing theory to radar imaging to obtain new theories,new systems and new methodologies of microwave imaging.This paper first summarizes the latest application of sparse microwave imaging,including Synthetic Aperture Radar(SAR),tomographic SAR and inverse SAR.As sparse signal processing keeps evolving,an avalanche of results have been obtained.We also highlight its recent theoretical advances,including structured sparsity,off-grid,Bayesian approaches,and point out new research directions in sparse microwave imaging.
基金National Natural Science Foundation of China(Grant Nos. 11271050 and 11371183)
文摘We consider the block orthogonal multi-matching pursuit(BOMMP) algorithm for the recovery of block sparse signals.A sharp condition is obtained for the exact reconstruction of block K-sparse signals via the BOMMP algorithm in the noiseless case,based on the block restricted isometry constant(block-RIC).Moreover,we show that the sharp condition combining with an extra condition on the minimum l_2 norm of nonzero blocks of block K-sparse signals is sufficient to ensure the BOMMP algorithm selects at least one true block index at each iteration until all true block indices are selected in the noisy case.The significance of the results we obtain in this paper lies in the fact that making explicit use of block sparsity of block sparse signals can achieve better recovery performance than ignoring the additional structure in the problem as being in the conventional sense.
基金supported by the National Natural Science Foundation of China(61171137)
文摘A direction-of-arrival （DOA） estimation algorithm is presented based on covariance differencing and sparse signal recovery, in which the desired signal is embedded in noise with unknown covariance. The key point of the algorithm is to eliminate the noise component by forming the difference of original and transformed covariance matrix, as well as cast the DOA estimation considered as a sparse signal recovery problem. Concerning accuracy and complexity of estimation, the authors take a vectorization operation on difference matrix, and further enforce sparsity by reweighted l1-norm penalty. We utilize data-validation to select the regularization parameter properly. Meanwhile, a kind of symmetric grid division and refinement strategy is introduced to make the proposed algorithm effective and also to mitigate the effects of limiting estimates to a grid of spatial locations. Compared with the covariance-differencing-based multiple signal classification （MUSIC） method, the proposed is of salient features, including increased resolution, improved robustness to colored noise, distinguishing the false peaks easily, but with no requiring of prior knowledge of the number of sources.
基金supported by the National Natural Science Foundation of China(61201149)the 111 Project(B08004)the Fundamental Research Funds for the Central Universities
文摘Distributed compressed sensing （DCS） is an emerging research field which exploits both intra-signal and inter-signal correlations. This paper focuses on the recovery of the sparse signals which can be modeled as joint sparsity model （JSM） 2 with different nonzero coefficients in the same location set. Smoothed L0 norm algorithm is utilized to convert a non-convex and intractable mixed L2,0 norm optimization problem into a solvable one. Compared with a series of single-measurement-vector problems, the proposed approach can obtain a better reconstruction performance by exploiting the inter-signal correlations. Simulation results show that our algorithm outperforms L1,1 norm optimization for both noiseless and noisy cases and is more robust against thermal noise compared with LI,2 recovery. Besides, with the help of the core concept of modified compressed sensing （CS） that utilizes partial known support as side information, we also extend this algorithm to decode correlated row sparse signals generated following JSM 1.
基金The authors are very grateful to the anonymous referees for their valuable comments and suggestions. We want to thank Mr. Liang Chen at Hunan University for many useful comments. This work was supported by the National Natural Science Foundation of China under Grant 11271117.
文摘This paper aims to investigate sufficient conditions for the recovery of sparse signals via the orthogonal matching pursuit （OMP） algorithm. In the noiseless case, we present a novel sufficient condition for the exact recovery of all k-sparse signals by the OMP algorithm, and demonstrate that this condition is sharp. In the noisy case, a sufficient condition for recovering the support of k-sparse signal is also presented. Generally, the computation for the restricted isometry constant （RIC） in these sufficient conditions is typically difficult, therefore we provide a new condition which is not only computable but also sufficient for the exact recovery of all k-sparse signals.
基金supported by the National Natural Science Foundation of China(grant nos.61907014,11871248,11701410,61901160)the Natural Science Foundation of Guangdong province(No.2021A1515010857)+2 种基金Youth Science Foundation of Henan Normal University(grant no.2019QK03)China Postdoctoral Science Foundation(grant no.2019M660557)Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme(2019).
文摘In countless applications,we need to reconstruct a K-sparse signal x∈R n from noisy measurements y=Φx+v,whereΦ∈R^(m×n)is a sensing matrix and v∈R m is a noise vector.Orthogonal least squares(OLS),which selects at each step the column that results in the most significant decrease in the residual power,is one of the most popular sparse recovery algorithms.In this paper,we investigate the number of iterations required for recovering x with the OLS algorithm.We show that OLS provides a stable reconstruction of all K-sparse signals x in[2.8K]iterations provided thatΦsatisfies the restricted isometry property(RIP).Our result provides a better recovery bound and fewer number of required iterations than those proposed by Foucart in 2013.
基金Supported by the National Natural Science Foundation of China(61501385)Science and Technology Planning Project of Sichuan Province,China(2016JY0242,2016GZ0210)Foundation of Southwest University of Science and Technology(15kftk02,15kffk01)
文摘Pulse signal recovery is to extract useful amplitude and time information from the pulse signal contaminated by noise. It is a great challenge to precisely recover the pulse signal in loud background noise. The conventional approaches,which are mostly based on the distribution of the pulse energy spectrum,do not well determine the locations and shapes of the pulses. In this paper,we propose a time domain method to reconstruct pulse signals. In the proposed approach,a sparse representation model is established to deal with the issue of the pulse signal recovery under noise conditions. The corresponding problem based on the sparse optimization model is solved by a matching pursuit algorithm. Simulations and experiments validate the effectiveness of the proposed approach on pulse signal recovery.
基金supported by the National Natural Science Foundation of China(6150117661201399)+1 种基金the Education Department of Heilongjiang Province Science and Technology Research Projects(12541638)the Developing Key Laboratory of Sensing Technology and Systems in Cold Region of Heilongjiang Province and Ministry of Education,(Heilongjiang University),P.R.China(P201408)
文摘For the direction of arrival（DOA） estimation,traditional sparse reconstruction methods for wideband signals usually need many iteration times.For this problem,a new method for two-dimensional wideband signals based on block sparse reconstruction is proposed.First,a prolate spheroidal wave function（PSWF） is used to fit the wideband signals,then the block sparse reconstruction technology is employed for DOA estimation.The proposed method uses orthogonalization to choose the matching atoms,ensuring that the residual components correspond to the minimum absolute value.Meanwhile,the vectors obtained by iteration are back-disposed according to the corresponding atomic matching rules,so the extra atoms are abandoned in the course of iteration,and the residual components of current iteration are reduced.Thus the original sparse signals are reconstructed.The proposed method reduces iteration times comparing with the traditional reconstruction methods,and the estimation precision is better than the classical two-sided correlation transformation（TCT）algorithm when the snapshot is small or the signal-to-noise ratio（SNR） is low.
基金partially supported by the Natural Science Foundation of Henan Province(Grant Nos.252300420326,242300420252)in part by the Key Scientifc Research Project of Colleges and Universities in Henan Province(Grant No.24A120007)+1 种基金in part by Training Program for Young Backbone Teachers in Higher Education Institutions of Henan Province(Grant No.2023GGJS037)in part by the National Natural Science Foundation of China(Grant Nos.12271215,12326378 and 11871248)。
文摘In many practical applications,we need to recover block sparse signals.In this paper,we encounter the system model where joint sparse signals exhibit block structure.To reconstruct this category of signals,we propose a new algorithm called block signal subspace matching pursuit(BSSMP)for the block joint sparse recovery problem in compressed sensing,which simultaneously reconstructs the support of block jointly sparse signals from a common sensing matrix.To begin with,we consider the case where block joint sparse matrix X has full column rank and any r nonzero rowblocks are linearly independent.Based on these assumptions,our theoretical analysis indicates that the BSSMP algorithm could reconstruct the support of X through at most K-r+[r/L]iterations if sensing matrix A satisfies the block restricted isometry property of order L(K-r)+r+1 with δB_(L(K-r)+r+1)<max{√r/√K+r/4+√r/4,√L/√Kd+√L}.This condition improves the existing result.
基金the Research Foundation for Doctoral Programs of Higher Education of China (Grant No.20060280003)the Shanghai Leading Academic Discipline Project (Grant No.T0102)
文摘In underdetermined blind source separation, more sources are to be estimated from less observed mixtures without knowing source signals and the mixing matrix. This paper presents a robust clustering algorithm for underdetermined blind separation of sparse sources with unknown number of sources in the presence of noise. It uses the robust competitive agglomeration （RCA） algorithm to estimate the source number and the mixing matrix, and the source signals then are recovered by using the interior point linear programming. Simulation results show good performance of the proposed algorithm for underdetermined blind sources separation （UBSS）.
基金supported by the National Natural Science Foundation of China(61171127)
文摘It is understood that the sparse signal recovery with a standard compressive sensing（CS） strategy requires the measurement matrix known as a priori. The measurement matrix is, however, often perturbed in a practical application.In order to handle such a case, an optimization problem by exploiting the sparsity characteristics of both the perturbations and signals is formulated. An algorithm named as the sparse perturbation signal recovery algorithm（SPSRA） is then proposed to solve the formulated optimization problem. The analytical results show that our SPSRA can simultaneously recover the signal and perturbation vectors by an alternative iteration way, while the convergence of the SPSRA is also analytically given and guaranteed. Moreover, the support patterns of the sparse signal and structured perturbation shown are the same and can be exploited to improve the estimation accuracy and reduce the computation complexity of the algorithm. The numerical simulation results verify the effectiveness of analytical ones.
基金supported by the National Natural Science Foundation of China(61907014,11871248,11701410,61901160)Youth Science Foundation of Henan Normal University(2019QK03).
文摘A greedy algorithm used for the recovery of sparse signals,multiple orthogonal least squares(MOLS)have recently attracted quite a big of attention.In this paper,we consider the number of iterations required for the MOLS algorithm for recovery of a K-sparse signal x∈R^(n).We show that MOLS provides stable reconstruction of all K-sparse signals x from y=Ax+w in|6K/ M|iterations when the matrix A satisfies the restricted isometry property(RIP)with isometry constantδ_(7K)≤0.094.Compared with the existing results,our sufficient condition is not related to the sparsity level K.
基金Supported by the National Key R&D Program of China(Grant No.2023YFA1009200)the National Natural Science Foundation of China(Grant Nos.12271079+1 种基金12494552)the Fundamental Research Funds for the Central Universities of China(Grant No.DUT24LAB127)。
文摘In this paper,we focus on the recovery of piecewise sparse signals containing both fast-decaying and slow-decaying nonzero entries.In order to improve the performance of classic Orthogonal Matching Pursuit(OMP)and Generalized Orthogonal Matching Pursuit(GOMP)algorithms for solving this problem,we propose the Piecewise Generalized Orthogonal Matching Pursuit(PGOMP)algorithm,by considering the mixed-decaying sparse signals as piecewise sparse signals with two components containing nonzero entries with different decay factors.The algorithm incorporates piecewise selection and deletion to retain the most significant entries according to the sparsity of each component.We provide a theoretical analysis based on the mutual coherence of the measurement matrix and the decay factors of the nonzero entries,establishing a sufficient condition for the PGOMP algorithm to select at least two correct indices in each iteration.Numerical simulations and an image decomposition experiment demonstrate that the proposed algorithm significantly improves the support recovery probability by effectively matching piecewise sparsity with decay factors.
文摘We consider the problem of constructing one sparse signal from a few measurements. This problem has been extensively addressed in the literature, providing many sub-optimal methods that assure convergence to a locally optimal solution under specific conditions. There are a few measurements associated with every signal, where the size of each measurement vector is less than the sparse signal＇s size. All of the sparse signals have the same unknown support. We generalize an existing algorithm for the recovery of one sparse signal from a single measurement to this problem and analyze its performances through simulations. We also compare the construction performance with other existing algorithms. Finally, the proposed method also shows advantages over the OMP （Orthogonal Matching Pursuit） algorithm in terms of the computational complexity.
