A novel Direction-Of-Arrival (DOA) estimation method is proposed in the presence of mutual coupling using the joint sparse recovery. In the proposed method, the eigenvector corresponding to the maximum eigenvalue of c...A novel Direction-Of-Arrival (DOA) estimation method is proposed in the presence of mutual coupling using the joint sparse recovery. In the proposed method, the eigenvector corresponding to the maximum eigenvalue of covariance matrix of array measurement is viewed as the signal to be represented. By exploiting the geometrical property in steering vectors and the symmetric Toeplitz structure of Mutual Coupling Matrix (MCM), the redundant dictionaries containing the DOA information are constructed. Consequently, the optimization model based on joint sparse recovery is built and then is solved through Second Order Cone Program (SOCP) and Interior Point Method (IPM). The DOA estimates are gotten according to the positions of nonzeros elements. At last, computer simulations demonstrate the excellent performance of the proposed method.展开更多
The traditional super-resolution direction finding methods based on sparse recovery need to divide the estimation space into several discrete angle grids, which will bring the final result some error. To this problem,...The traditional super-resolution direction finding methods based on sparse recovery need to divide the estimation space into several discrete angle grids, which will bring the final result some error. To this problem, a novel method for wideband signals by sparse recovery in the frequency domain is proposed. The optimization functions are found and solved by the received data at every frequency, on this basis, the sparse support set is obtained, then the direction of arrival (DOA) is acquired by integrating the information of all frequency bins, and the initial signal can also be recovered. This method avoids the error caused by sparse recovery methods based on grid division, and the degree of freedom is also expanded by array transformation, especially it has a preferable performance under the circumstances of a small number of snapshots and a low signal to noise ratio (SNR).展开更多
In order to improve the performance of linear time-varying（LTV）channel estimation,based on the sparsity of channel taps in time domain,a sparse recovery method of LTV channel in orthogonal frequency division multipl...In order to improve the performance of linear time-varying（LTV）channel estimation,based on the sparsity of channel taps in time domain,a sparse recovery method of LTV channel in orthogonal frequency division multiplexing（OFDM）system is proposed.Firstly,based on the compressive sensing theory,the average of the channel taps over one symbol duration in the LTV channel model is estimated.Secondly,in order to deal with the inter-carrier interference（ICI）,the group-pilot design criterion is used based on the minimization of mutual coherence of the measurement.Finally,an efficient pilot pattern optimization algorithm is proposed by a dual layer loops iteration.The simulation results show that the new method uses less pilots,has a smaller bit error ratio（BER）,and greater ability to deal with Doppler frequency shift than the traditional method does.展开更多
Sparse recovery(or sparse representation) is a widely studied issue in the fields of signal processing, image processing, computer vision, machine learning and so on, since signals such as videos and images, can be sp...Sparse recovery(or sparse representation) is a widely studied issue in the fields of signal processing, image processing, computer vision, machine learning and so on, since signals such as videos and images, can be sparsely represented under some frames. Most of fast algorithms at present are based on solving l0or l1minimization problems and they are efficient in sparse recovery. However, the theoretically sufficient conditions on the sparsity of the signal for l0or l1minimization problems and algorithms are too strict. In some applications, there are signals with structures, i.e., the nonzero entries have some certain distribution. In this paper,we consider the uniqueness and feasible conditions for piecewise sparse recovery. Piecewise sparsity means that the sparse signal x is a union of several sparse sub-signals xi(i=1, 2,..., N),i.e., x=(x_(1)^(T), x_(2)^(T),..., x_(N)^(T))T, corresponding to the measurement matrix A which is composed of union of bases A=[A_(1), A_(2),..., A_(N)]. We introduce the mutual coherence for the sub-matrices Ai(i = 1, 2,..., N) by considering the block structure of A corresponding to piecewise sparse signal x, to study the new upper bounds of ‖x‖0(number of nonzero entries of signal) recovered by both l0and l1optimizations. The structured information of measurement matrix A is exploited to improve the sufficient conditions for successfully piecewise sparse recovery and also improve the reliability of l0and l1optimization models on recovering global sparse vectors.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 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 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
In this paper,we offer a new sparse recovery strategy based on the generalized error function.The introduced penalty function involves both the shape and the scale parameters,making it extremely flexible.For both cons...In this paper,we offer a new sparse recovery strategy based on the generalized error function.The introduced penalty function involves both the shape and the scale parameters,making it extremely flexible.For both constrained and unconstrained models,the theoretical analysis results in terms of the null space property,the spherical section property and the restricted invertibility factor are established.The practical algorithms via both the iteratively reweighted■_(1)and the difference of convex functions algorithms are presented.Numerical experiments are carried out to demonstrate the benefits of the suggested approach in a variety of circumstances.Its practical application in magnetic resonance imaging(MRI)reconstruction is also investigated.展开更多
This paper is concerned with the structured simultaneous low-rank and sparse recovery,which can be formulated as the rank and zero-norm regularized least squares problem with a hard constraint diag(■)=0.For this clas...This paper is concerned with the structured simultaneous low-rank and sparse recovery,which can be formulated as the rank and zero-norm regularized least squares problem with a hard constraint diag(■)=0.For this class of NP-hard problems,we propose a convex relaxation algorithm by applying the accelerated proximal gradient method to a convex relaxation model,which is yielded by the smoothed nuclear norm and the weighted l1-norm regularized least squares problem.A theoretical guarantee is provided by establishing the error bounds of the iterates to the true solution under mild restricted strong convexity conditions.To the best of our knowledge,this work is the first one to characterize the error bound of the iterates of the algorithm to the true solution.Finally,numerical results are reported for some random test problems and synthetic data in subspace clustering to verify the efficiency of the proposed convex relaxation algorithm.展开更多
In this paper,by combining the inertial technique and the gradient descent method with Polyak's stepsizes,we propose a novel inertial self-adaptive gradient algorithm to solve the split feasi-bility problem in Hil...In this paper,by combining the inertial technique and the gradient descent method with Polyak's stepsizes,we propose a novel inertial self-adaptive gradient algorithm to solve the split feasi-bility problem in Hilbert spaces and prove some strong and weak convergence theorems of our method under standard assumptions.We examine the performance of our method on the sparse recovery prob-lem beside an example in an infinite dimensional Hilbert space with synthetic data and give some numerical results to show the potential applicability of the proposed method and comparisons with related methods emphasize it further.展开更多
In some applications,there are signals with piecewise structure to be recovered.In this paper,we propose a piecewise_ISS(P_ISS)method which aims to preserve the piecewise sparse structure(or the small-scaled entries)o...In some applications,there are signals with piecewise structure to be recovered.In this paper,we propose a piecewise_ISS(P_ISS)method which aims to preserve the piecewise sparse structure(or the small-scaled entries)of piecewise signals.In order to avoid selecting redundant false small-scaled elements,we also implement the piecewise_ISS algorithm in parallel and distributed manners equipped with a deletion rule.Numerical experiments indicate that compared with alSS,the P_ISS algorithm is more effective and robust for piecewise sparse recovery.展开更多
Joint sparse recovery(JSR)in compressed sensing(CS)is to simultaneously recover multiple jointly sparse vectors from their incomplete measurements that are conducted based on a common sensing matrix.In this study,the ...Joint sparse recovery(JSR)in compressed sensing(CS)is to simultaneously recover multiple jointly sparse vectors from their incomplete measurements that are conducted based on a common sensing matrix.In this study,the focus is placed on the rank defective case where the number of measurements is limited or the signals are significantly correlated with each other.First,an iterative atom refinement process is adopted to estimate part of the atoms of the support set.Subsequently,the above atoms along with the measurements are used to estimate the remaining atoms.The estimation criteria for atoms are based on the principle of minimum subspace distance.Extensive numerical experiments were performed in noiseless and noisy scenarios,and results reveal that iterative subspace matching pursuit(ISMP)outperforms other existing algorithms for JSR.展开更多
Motivated by the study of regularization for sparse problems,we propose a new regularization method for sparse vector recovery.We derive sufficient conditions on the well-posedness of the new regularization,and design...Motivated by the study of regularization for sparse problems,we propose a new regularization method for sparse vector recovery.We derive sufficient conditions on the well-posedness of the new regularization,and design an iterative algorithm,namely the iteratively reweighted algorithm(IR-algorithm),for efficiently computing the sparse solutions to the proposed regularization model.The convergence of the IR-algorithm and the setting of the regularization parameters are analyzed at length.Finally,we present numerical examples to illustrate the features of the new regularization and algorithm.展开更多
In this paper, we propose a novel source localization method to estimate parameters of arbitrary field sources, which may lie in near-field region or far-field region of array aperture. The proposed method primarily c...In this paper, we propose a novel source localization method to estimate parameters of arbitrary field sources, which may lie in near-field region or far-field region of array aperture. The proposed method primarily constructs two special spatial-temporal covariance matrixes which can avoid the array aperture loss, and then estimates the frequencies of signals to obtain the oblique projection matrixes. By using the oblique projection technique, the covariance matrixes can be transformed into several data matrixes which only contain single source information, respectively. At last, based on the sparse signal recovery method, these data matrixes are utilized to solve the source localization problem. Compared with the existing typical source localization algorithms, the proposed method improves the estimation accuracy, and provides higher angle resolution for closely spaced sources scenario. Simulation results are given to demonstrate the performance of the proposed algorithm.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
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
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
To tackle the challenges of intractable parameter tun-ing,significant computational expenditure and imprecise model-driven sparse-based direction of arrival(DOA)estimation with array error(AE),this paper proposes a de...To tackle the challenges of intractable parameter tun-ing,significant computational expenditure and imprecise model-driven sparse-based direction of arrival(DOA)estimation with array error(AE),this paper proposes a deep unfolded amplitude-phase error self-calibration network.Firstly,a sparse-based DOA model with an array convex error restriction is established,which gets resolved via an alternating iterative minimization(AIM)algo-rithm.The algorithm is then unrolled to a deep network known as AE-AIM Network(AE-AIM-Net),where all parameters are opti-mized through multi-task learning using the constructed com-plete dataset.The results of the simulation and theoretical analy-sis suggest that the proposed unfolded network achieves lower computational costs compared to typical sparse recovery meth-ods.Furthermore,it maintains excellent estimation performance even in the presence of array magnitude-phase errors.展开更多
Given the measurement matrix A and the observation signal y,the central purpose of compressed sensing is to find the most sparse solution of the underdetermined linear system y=Ax+z,where x is the s-sparse signal to b...Given the measurement matrix A and the observation signal y,the central purpose of compressed sensing is to find the most sparse solution of the underdetermined linear system y=Ax+z,where x is the s-sparse signal to be recovered and z is the noise vector.Zhou and Yu[Front.Appl.Math.Stat.,5(2019),Article 14]recently proposed a novel non-convex weighted l_(r)-l_(2)minimization method for effective sparse recovery.In this paper,under newly coherence-based conditions,we study the non-convex weighted l_(r)-l_(2)minimization in reconstructing sparse signals that are contaminated by different noises.Concretely,the results reveal that if the coherenceμof measurement matrix A fulfillsμ<k(s;r,α,N),s>1,α^(1/r)N(1/2)<1,then any s-sparse signals in the noisy scenarios could be ensured to be reconstructed robustly by solving weighted l_(r)-l_(2)minimization non-convex optimization problem.Furthermore,some central remarks are presented to clear that the reconstruction assurance is much weaker than the existing ones.To the best of our knowledge,this is the first mutual coherence-based sufficient condition for such approach.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
基金Supported by the Innovation Foundation for Outstanding Postgraduates in the Electronic Engineering Institute of PLA (No. 2009YB005)
文摘A novel Direction-Of-Arrival (DOA) estimation method is proposed in the presence of mutual coupling using the joint sparse recovery. In the proposed method, the eigenvector corresponding to the maximum eigenvalue of covariance matrix of array measurement is viewed as the signal to be represented. By exploiting the geometrical property in steering vectors and the symmetric Toeplitz structure of Mutual Coupling Matrix (MCM), the redundant dictionaries containing the DOA information are constructed. Consequently, the optimization model based on joint sparse recovery is built and then is solved through Second Order Cone Program (SOCP) and Interior Point Method (IPM). The DOA estimates are gotten according to the positions of nonzeros elements. At last, computer simulations demonstrate the excellent performance of the proposed method.
基金supported by the National Natural Science Foundation of China(61501176)University Nursing Program for Young Scholars with Creative Talents in Heilongjiang Province(UNPYSCT-2016017)
文摘The traditional super-resolution direction finding methods based on sparse recovery need to divide the estimation space into several discrete angle grids, which will bring the final result some error. To this problem, a novel method for wideband signals by sparse recovery in the frequency domain is proposed. The optimization functions are found and solved by the received data at every frequency, on this basis, the sparse support set is obtained, then the direction of arrival (DOA) is acquired by integrating the information of all frequency bins, and the initial signal can also be recovered. This method avoids the error caused by sparse recovery methods based on grid division, and the degree of freedom is also expanded by array transformation, especially it has a preferable performance under the circumstances of a small number of snapshots and a low signal to noise ratio (SNR).
基金Supported by the National Natural Science Foundation of China(61571368)the Ministerial Level Advanced Research Foundation(950303HK,C9149C0511)
文摘In order to improve the performance of linear time-varying（LTV）channel estimation,based on the sparsity of channel taps in time domain,a sparse recovery method of LTV channel in orthogonal frequency division multiplexing（OFDM）system is proposed.Firstly,based on the compressive sensing theory,the average of the channel taps over one symbol duration in the LTV channel model is estimated.Secondly,in order to deal with the inter-carrier interference（ICI）,the group-pilot design criterion is used based on the minimization of mutual coherence of the measurement.Finally,an efficient pilot pattern optimization algorithm is proposed by a dual layer loops iteration.The simulation results show that the new method uses less pilots,has a smaller bit error ratio（BER）,and greater ability to deal with Doppler frequency shift than the traditional method does.
基金Supported by the National Natural Science Foundation of China (Grant Nos.1187113711572081)the Fundamental Research Funds for the Central Universities of China (Grant No.QYWKC2018007)。
文摘Sparse recovery(or sparse representation) is a widely studied issue in the fields of signal processing, image processing, computer vision, machine learning and so on, since signals such as videos and images, can be sparsely represented under some frames. Most of fast algorithms at present are based on solving l0or l1minimization problems and they are efficient in sparse recovery. However, the theoretically sufficient conditions on the sparsity of the signal for l0or l1minimization problems and algorithms are too strict. In some applications, there are signals with structures, i.e., the nonzero entries have some certain distribution. In this paper,we consider the uniqueness and feasible conditions for piecewise sparse recovery. Piecewise sparsity means that the sparse signal x is a union of several sparse sub-signals xi(i=1, 2,..., N),i.e., x=(x_(1)^(T), x_(2)^(T),..., x_(N)^(T))T, corresponding to the measurement matrix A which is composed of union of bases A=[A_(1), A_(2),..., A_(N)]. We introduce the mutual coherence for the sub-matrices Ai(i = 1, 2,..., N) by considering the block structure of A corresponding to piecewise sparse signal x, to study the new upper bounds of ‖x‖0(number of nonzero entries of signal) recovered by both l0and l1optimizations. The structured information of measurement matrix A is exploited to improve the sufficient conditions for successfully piecewise sparse recovery and also improve the reliability of l0and l1optimization models on recovering global sparse vectors.
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.
基金supported by the Zhejiang Provincial Natural Science Foundation of China under grant No.LQ21A010003.
文摘In this paper,we offer a new sparse recovery strategy based on the generalized error function.The introduced penalty function involves both the shape and the scale parameters,making it extremely flexible.For both constrained and unconstrained models,the theoretical analysis results in terms of the null space property,the spherical section property and the restricted invertibility factor are established.The practical algorithms via both the iteratively reweighted■_(1)and the difference of convex functions algorithms are presented.Numerical experiments are carried out to demonstrate the benefits of the suggested approach in a variety of circumstances.Its practical application in magnetic resonance imaging(MRI)reconstruction is also investigated.
基金This work is supported by the National Natural Science Foundation of China(Nos.61402182 and 61273295).
文摘This paper is concerned with the structured simultaneous low-rank and sparse recovery,which can be formulated as the rank and zero-norm regularized least squares problem with a hard constraint diag(■)=0.For this class of NP-hard problems,we propose a convex relaxation algorithm by applying the accelerated proximal gradient method to a convex relaxation model,which is yielded by the smoothed nuclear norm and the weighted l1-norm regularized least squares problem.A theoretical guarantee is provided by establishing the error bounds of the iterates to the true solution under mild restricted strong convexity conditions.To the best of our knowledge,this work is the first one to characterize the error bound of the iterates of the algorithm to the true solution.Finally,numerical results are reported for some random test problems and synthetic data in subspace clustering to verify the efficiency of the proposed convex relaxation algorithm.
基金funded by University of Transport and Communications (UTC) under Grant Number T2023-CB-001
文摘In this paper,by combining the inertial technique and the gradient descent method with Polyak's stepsizes,we propose a novel inertial self-adaptive gradient algorithm to solve the split feasi-bility problem in Hilbert spaces and prove some strong and weak convergence theorems of our method under standard assumptions.We examine the performance of our method on the sparse recovery prob-lem beside an example in an infinite dimensional Hilbert space with synthetic data and give some numerical results to show the potential applicability of the proposed method and comparisons with related methods emphasize it further.
基金National Natural Science Foundation of China(Nos.11871137,11471066,11290143)the Fundamental Research of Civil Aircraft(No.MJ-F-2012-04)。
文摘In some applications,there are signals with piecewise structure to be recovered.In this paper,we propose a piecewise_ISS(P_ISS)method which aims to preserve the piecewise sparse structure(or the small-scaled entries)of piecewise signals.In order to avoid selecting redundant false small-scaled elements,we also implement the piecewise_ISS algorithm in parallel and distributed manners equipped with a deletion rule.Numerical experiments indicate that compared with alSS,the P_ISS algorithm is more effective and robust for piecewise sparse recovery.
基金supported by the National Natural Science Foundation of China(61771258)the Postgraduate Research and Practice Innovation Program of Jiangsu Province(KYCX 210749)。
文摘Joint sparse recovery(JSR)in compressed sensing(CS)is to simultaneously recover multiple jointly sparse vectors from their incomplete measurements that are conducted based on a common sensing matrix.In this study,the focus is placed on the rank defective case where the number of measurements is limited or the signals are significantly correlated with each other.First,an iterative atom refinement process is adopted to estimate part of the atoms of the support set.Subsequently,the above atoms along with the measurements are used to estimate the remaining atoms.The estimation criteria for atoms are based on the principle of minimum subspace distance.Extensive numerical experiments were performed in noiseless and noisy scenarios,and results reveal that iterative subspace matching pursuit(ISMP)outperforms other existing algorithms for JSR.
基金Project supported by the National Natural Science Foundation of China(No.61603322)the Research Foundation of Education Bureau of Hunan Province of China(No.16C1542)
文摘Motivated by the study of regularization for sparse problems,we propose a new regularization method for sparse vector recovery.We derive sufficient conditions on the well-posedness of the new regularization,and design an iterative algorithm,namely the iteratively reweighted algorithm(IR-algorithm),for efficiently computing the sparse solutions to the proposed regularization model.The convergence of the IR-algorithm and the setting of the regularization parameters are analyzed at length.Finally,we present numerical examples to illustrate the features of the new regularization and algorithm.
基金supported by the National Natural Science Foundation of China (60901060)
文摘In this paper, we propose a novel source localization method to estimate parameters of arbitrary field sources, which may lie in near-field region or far-field region of array aperture. The proposed method primarily constructs two special spatial-temporal covariance matrixes which can avoid the array aperture loss, and then estimates the frequencies of signals to obtain the oblique projection matrixes. By using the oblique projection technique, the covariance matrixes can be transformed into several data matrixes which only contain single source information, respectively. At last, based on the sparse signal recovery method, these data matrixes are utilized to solve the source localization problem. Compared with the existing typical source localization algorithms, the proposed method improves the estimation accuracy, and provides higher angle resolution for closely spaced sources scenario. Simulation results are given to demonstrate the performance of the proposed algorithm.
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.
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.
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(62301598).
文摘To tackle the challenges of intractable parameter tun-ing,significant computational expenditure and imprecise model-driven sparse-based direction of arrival(DOA)estimation with array error(AE),this paper proposes a deep unfolded amplitude-phase error self-calibration network.Firstly,a sparse-based DOA model with an array convex error restriction is established,which gets resolved via an alternating iterative minimization(AIM)algo-rithm.The algorithm is then unrolled to a deep network known as AE-AIM Network(AE-AIM-Net),where all parameters are opti-mized through multi-task learning using the constructed com-plete dataset.The results of the simulation and theoretical analy-sis suggest that the proposed unfolded network achieves lower computational costs compared to typical sparse recovery meth-ods.Furthermore,it maintains excellent estimation performance even in the presence of array magnitude-phase errors.
基金supported in part by the National Natural Science Foundation of China(Grant Nos.12101454,12101512,12071380,62063031)by the Chongqing Normal University Foundation Project(Grant No.23XLB013)+8 种基金by the Fuxi Scientific Research Innovation Team of Tianshui Normal University(Grant No.FXD2020-03)by the National Natural Science Foundation of China(Grant No.12301594)by the China Postdoctoral Science Foundation(Grant No.2021M692681)by the Natural Science Foundation of Chongqing,China(Grant No.cstc2021jcyj-bshX0155)by the Fundamental Research Funds for the Central Universities(Grant No.SWU120078)by the Natural Science Foundation of Gansu Province(Grant No.21JR1RE292)by the College Teachers Innovation Foundation of Gansu Province(Grant No.2023B-132)by the Joint Funds of the Natural Science Innovation-driven development of Chongqing(Grant No.2023NSCQ-LZX0218)by the Chongqing Talent Project(Grant No.cstc2021ycjh-bgzxm0015).
文摘Given the measurement matrix A and the observation signal y,the central purpose of compressed sensing is to find the most sparse solution of the underdetermined linear system y=Ax+z,where x is the s-sparse signal to be recovered and z is the noise vector.Zhou and Yu[Front.Appl.Math.Stat.,5(2019),Article 14]recently proposed a novel non-convex weighted l_(r)-l_(2)minimization method for effective sparse recovery.In this paper,under newly coherence-based conditions,we study the non-convex weighted l_(r)-l_(2)minimization in reconstructing sparse signals that are contaminated by different noises.Concretely,the results reveal that if the coherenceμof measurement matrix A fulfillsμ<k(s;r,α,N),s>1,α^(1/r)N(1/2)<1,then any s-sparse signals in the noisy scenarios could be ensured to be reconstructed robustly by solving weighted l_(r)-l_(2)minimization non-convex optimization problem.Furthermore,some central remarks are presented to clear that the reconstruction assurance is much weaker than the existing ones.To the best of our knowledge,this is the first mutual coherence-based sufficient condition for such approach.
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.
