The aim of this paper is to prove another variation on the Heisenberg uncertainty principle,we generalize the quantitative uncertainty relations in n different(time-frequency)domains and we will give an algorithm for ...The aim of this paper is to prove another variation on the Heisenberg uncertainty principle,we generalize the quantitative uncertainty relations in n different(time-frequency)domains and we will give an algorithm for the signal recovery related to the canonical Fourier-Bessel transform.展开更多
Stochastic resonance（SR） enhances the nonlinear system behavior with the assistance of noise, including the sensitivity and selectivity of the response to the exterior stimulus. The energy-transfer mechanism makes t...Stochastic resonance（SR） enhances the nonlinear system behavior with the assistance of noise, including the sensitivity and selectivity of the response to the exterior stimulus. The energy-transfer mechanism makes the weak information revealed in the output spectrum, while the time-waveform is distorted. The distortion analysis was made both from the particle＇s dynan-fics and signal processing. The factors causing the deviation in the output are presented and the function of the recovery system is proposed. By the investigation of the particle＇s motion track in the bistable system and the suggested recovery system, the influences of noise and system parameters on the recovery course were discussed. Moreover, the pulse distortion appearing the recovery waveform caused by the particle＇s transitions at the bistable potential＇ inflexions was explained. Due to different characteristics, cascaded-bistable SR or mono-stable SR was introduced to process different types of signals. The final recovery signal is just the suggested recovery system＇s response to the SR output. Meanwhile, the recovery system is optional, as parameter-tuned or parameter-fixed. Since the method requires no average processing, it is applicable to a single sample with limited length. The numerical simulations reveal that the SR recovery method can recover the waveform containing weak information submerged ha noise effectively. The engineering application to the vibration analysis of metal cutting chose the combination of mono-stable SR and the parameter-fixed recovery system. Because the optimal SR state is not required strongly, the system parameters are tuned in a wider range than the traditional SR processing methods.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 study is given on the application of BP neural network (BPNN) in sensorfailure detection in control systems, and on the networ architecture desgn, the redun-dancy,the quickness and the insensitivity to sensor noise ...A study is given on the application of BP neural network (BPNN) in sensorfailure detection in control systems, and on the networ architecture desgn, the redun-dancy,the quickness and the insensitivity to sensor noise of the BPNN based sensor detec-tion methed. Besules, an exploration is made into tbe factors accounting for the quality ofsignal recovery for failed sensor using BPNN. The results reveal clearly that BPNN can besuccessfully used in sensor failure detection and data recovery.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
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
Optical chaos offers a promising approach to establishing secure communication at high data rates in a shared physical channel,like optical fibers and free space.However,the required synchronization between the transm...Optical chaos offers a promising approach to establishing secure communication at high data rates in a shared physical channel,like optical fibers and free space.However,the required synchronization between the transmitter and the receiver can be severely impaired by the nonidealities of the optical link.In particular,free-space optical communications are affected by atmospheric turbulence,which causes beam scintillation and results in time-varying fading of the optical intensity at the receiver side.In this work,we investigate experimentally the propagation of a chaotic signal in an indoor optical link with controllable synthetic turbulence,and we show that the degradation of chaos properties caused by the turbulent environment can be fully mitigated in the optical domain using an adaptive multi-aperture receiver.The proposed receiver integrates a two-dimensional array of optical antennas and a programmable optical processor(POP)on a silicon photonic platform.With respect to a conventional single-aperture receiver,the POP-assisted receiver recovers the complex dynamics of the optical chaos,ensuring a high degree of correlation between the transmitted signal and the received signal,even for a high degree of turbulence.Our results demonstrate the possibility of establishing and maintaining reliable,secure communication in a chaos-based cryptosystem in a free space optical link of km-range length.展开更多
We propose the Dantzig selector based on the l_(1-q)(1<q≤2)minimization model for the sparse signal recovery.First,we discuss some properties of l_(1-q)minimization model and give some useful inequalities.Then,we ...We propose the Dantzig selector based on the l_(1-q)(1<q≤2)minimization model for the sparse signal recovery.First,we discuss some properties of l_(1-q)minimization model and give some useful inequalities.Then,we give a sufficient condition based on the restricted isometry property for the stable recovery of signals.The l_(1-2)minimization model of Yin-Lou-He is extended to the l_(1-q)minimization model.展开更多
Large dynamic range and ultra-wideband receiving abilities are significant for many receivers. With these abilities, receivers can obtain signals with different power in ultra-wideband frequency space without informat...Large dynamic range and ultra-wideband receiving abilities are significant for many receivers. With these abilities, receivers can obtain signals with different power in ultra-wideband frequency space without information loss. However, conventional receiving scheme is hard to have large dynamic range and ultra-wideband receiving simultaneously because of the analog-to-digital converter(ADC) dynamic range and sample rate limitations. In this paper, based on the modulated sampling and unlimited sampling, a novel receiving scheme is proposed to achieve large dynamic range and ultra-wideband receiving. Focusing on the single carrier signals, the proposed scheme only uses a single self-rest ADC(SR-ADC) with low sample rate, and it achieves large dynamic range and ultra-wideband receiving simultaneously. Two receiving scenarios are considered, and they are cooperative strong signal receiving and non-cooperative strong/weak signals receiving. In the cooperative receiving scenario, an improved fast recovery method is proposed to obtain the modulated sampling output. In the non-cooperative receiving scenario, the strong and weak signals with different carrier frequencies are considered, and the signal processing method can recover and estimate each signal. Simulation results show that the proposed scheme can realize large dynamic range and ultra-wideband receiving simultaneously when the input signal-to-noise(SNR) ratio is high.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
A convex variational formulation is proposed to solve multicomponent signal processing problems in Hilbert spaces.The cost function consists of a separable term, in which each component is modeled through its own pote...A convex variational formulation is proposed to solve multicomponent signal processing problems in Hilbert spaces.The cost function consists of a separable term, in which each component is modeled through its own potential,and of a coupling term, in which constraints on linear transformations of the components are penalized with smooth functionals.An algorithm with guaranteed weak convergence to a solution to the problem is provided.Various multicomponent signal decomposition and recovery applications are discussed.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
An algorithm for recovering the quaternion signals in both noiseless and noise contaminated scenarios by solving an L1-norm minimization problem is presented. The L1-norm minimization problem over the quaternion numbe...An algorithm for recovering the quaternion signals in both noiseless and noise contaminated scenarios by solving an L1-norm minimization problem is presented. The L1-norm minimization problem over the quaternion number field is solved by converting it to an equivalent second-order cone programming problem over the real number field, which can be readily solved by convex optimization solvers like SeDuMi. Numerical experiments are provided to illustrate the effectiveness of the proposed algorithm. In a noiseless scenario, the experimental results show that under some practically acceptable conditions, exact signal recovery can be achieved. With additive noise contamination in measurements, the experimental results show that the proposed algorithm is robust to noise. The proposed algorithm can be applied in compressed-sensing-based signal recovery in the quaternion domain.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
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
This paper considers a corrupted compressed sensing problem and is devoted to recover signals that are approximately sparse in some general dictionary but corrupted by a combination of interference having a sparse rep...This paper considers a corrupted compressed sensing problem and is devoted to recover signals that are approximately sparse in some general dictionary but corrupted by a combination of interference having a sparse representation in a second general dictionary and measurement noise.We provide new restricted isometry property(RIP)analysis to achieve stable recovery of sparsely corrupted signals through Justice Pursuit De-Noising(JPDN)with an additional parameter.Our main tool is to adapt a crucial sparse decomposition technique to the analysis of the Justice Pursuit method.The proposed RIP condition improves the existing representative results.Numerical simulations are provided to verify the reliability of the JPDN model.展开更多
Aiming at the problem that the positioning accuracy of WiFi indoor positioning technology based on location fingerprint has not reached the requirements of practical application, a WiFi indoor positioning and tracking...Aiming at the problem that the positioning accuracy of WiFi indoor positioning technology based on location fingerprint has not reached the requirements of practical application, a WiFi indoor positioning and tracking algorithm combining adaptive affine propagation (AAPC), compressed sensing (CS) and Kalman filter is proposed. In the off-line phase, AAPC algorithm is used to generate clustering fingerprints with optimal clustering effect performance;In the online phase, CS and nearest neighbor algorithm are used for position estimation;Finally, the Kalman filter and physical constraints are combined to perform positioning and tracking. By collecting a large number of real experimental data, it is proved that the developed algorithm has higher positioning accuracy and more accurate trajectory tracking effect.展开更多
This paper concentrates on super-resolution imaging of the ship target under the sparse aperture situation.Firstly,a multi-static configuration is utilized to solve the coherent processing interval(CPI)problem caused ...This paper concentrates on super-resolution imaging of the ship target under the sparse aperture situation.Firstly,a multi-static configuration is utilized to solve the coherent processing interval(CPI)problem caused by the slow-speed motion of ship targets.Then,we realize signal restoration and image reconstruction with the alternating direction method of multipliers(ADMM).Furthermore,we adopt the interferometric technique to produce the three-dimensional(3D)images of ship targets,namely interferometric inverse synthetic aperture radar(InISAR)imaging.Experiments based on the simulated data are utilized to verify the validity of the proposed method.展开更多
In an earlier work, we proposed a frame-based kernel analysis approach to the problem of recovering erasures from unknown locations. The new approach led to the stability question on recovering a signal from noisy par...In an earlier work, we proposed a frame-based kernel analysis approach to the problem of recovering erasures from unknown locations. The new approach led to the stability question on recovering a signal from noisy partial frame coefficients with erasures occurring at unknown locations. In this continuing work, we settle this problem by obtaining a complete characterization of frames that provide stable reconstructions. We show that an encoding frame provides a stable signal recovery from noisy partial frame coefficients at unknown locations if and only if it is totally robust with respect to erasures. We present several characterizations for either totally robust frames or almost robust frames. Based on these characterizations several explicit construction algorithms for totally robust and almost robust frames are proposed. As a consequence of the construction methods, we obtain that the probability for a randomly generated frame to be totally robust with respect to a fixed number of erasures is one.展开更多
文摘The aim of this paper is to prove another variation on the Heisenberg uncertainty principle,we generalize the quantitative uncertainty relations in n different(time-frequency)domains and we will give an algorithm for the signal recovery related to the canonical Fourier-Bessel transform.
基金supported by National Hi-tech Research and Development Program of China (863 Program, Grant No. 2007AA04Z414)National Natural Science Foundation of China (Grant No. 50675153)+1 种基金Tianjin Municipal Natural Science Foundation of China (Grant No. 07JCYBJC04600)Specialized Research Fund for Doctoral Program of Higher Education of China (Grant No. 20060056016)
文摘Stochastic resonance（SR） enhances the nonlinear system behavior with the assistance of noise, including the sensitivity and selectivity of the response to the exterior stimulus. The energy-transfer mechanism makes the weak information revealed in the output spectrum, while the time-waveform is distorted. The distortion analysis was made both from the particle＇s dynan-fics and signal processing. The factors causing the deviation in the output are presented and the function of the recovery system is proposed. By the investigation of the particle＇s motion track in the bistable system and the suggested recovery system, the influences of noise and system parameters on the recovery course were discussed. Moreover, the pulse distortion appearing the recovery waveform caused by the particle＇s transitions at the bistable potential＇ inflexions was explained. Due to different characteristics, cascaded-bistable SR or mono-stable SR was introduced to process different types of signals. The final recovery signal is just the suggested recovery system＇s response to the SR output. Meanwhile, the recovery system is optional, as parameter-tuned or parameter-fixed. Since the method requires no average processing, it is applicable to a single sample with limited length. The numerical simulations reveal that the SR recovery method can recover the waveform containing weak information submerged ha noise effectively. The engineering application to the vibration analysis of metal cutting chose the combination of mono-stable SR and the parameter-fixed recovery system. Because the optimal SR state is not required strongly, the system parameters are tuned in a wider range than the traditional SR processing methods.
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.
文摘A study is given on the application of BP neural network (BPNN) in sensorfailure detection in control systems, and on the networ architecture desgn, the redun-dancy,the quickness and the insensitivity to sensor noise of the BPNN based sensor detec-tion methed. Besules, an exploration is made into tbe factors accounting for the quality ofsignal recovery for failed sensor using BPNN. The results reveal clearly that BPNN can besuccessfully used in sensor failure detection and data recovery.
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 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 Direction Générale de l’Armement(DGA),the European Office of Aerospace Research and Development(FA8655-22-1-7032)the Chair in Photonics.A.Ma.,F.M.support from the Italian National Recovery and Resilience Plan(NRRP)of NextGenerationEU,partnership on“Telecommunications of the Future”(PE00000001—program“RESTART”,Structural Project“Rigoletto”and Focused Project“HePIC”)(https://www.polifab.polimi.it/).
文摘Optical chaos offers a promising approach to establishing secure communication at high data rates in a shared physical channel,like optical fibers and free space.However,the required synchronization between the transmitter and the receiver can be severely impaired by the nonidealities of the optical link.In particular,free-space optical communications are affected by atmospheric turbulence,which causes beam scintillation and results in time-varying fading of the optical intensity at the receiver side.In this work,we investigate experimentally the propagation of a chaotic signal in an indoor optical link with controllable synthetic turbulence,and we show that the degradation of chaos properties caused by the turbulent environment can be fully mitigated in the optical domain using an adaptive multi-aperture receiver.The proposed receiver integrates a two-dimensional array of optical antennas and a programmable optical processor(POP)on a silicon photonic platform.With respect to a conventional single-aperture receiver,the POP-assisted receiver recovers the complex dynamics of the optical chaos,ensuring a high degree of correlation between the transmitted signal and the received signal,even for a high degree of turbulence.Our results demonstrate the possibility of establishing and maintaining reliable,secure communication in a chaos-based cryptosystem in a free space optical link of km-range length.
基金supported by the National Natural Science Foundation of China“Variable exponential function spaces on variable anisotropic Euclidean spaces and their applications”(12261083),“Harmonic analysis on affine symmetric spaces”(12161083).
文摘We propose the Dantzig selector based on the l_(1-q)(1<q≤2)minimization model for the sparse signal recovery.First,we discuss some properties of l_(1-q)minimization model and give some useful inequalities.Then,we give a sufficient condition based on the restricted isometry property for the stable recovery of signals.The l_(1-2)minimization model of Yin-Lou-He is extended to the l_(1-q)minimization model.
文摘Large dynamic range and ultra-wideband receiving abilities are significant for many receivers. With these abilities, receivers can obtain signals with different power in ultra-wideband frequency space without information loss. However, conventional receiving scheme is hard to have large dynamic range and ultra-wideband receiving simultaneously because of the analog-to-digital converter(ADC) dynamic range and sample rate limitations. In this paper, based on the modulated sampling and unlimited sampling, a novel receiving scheme is proposed to achieve large dynamic range and ultra-wideband receiving. Focusing on the single carrier signals, the proposed scheme only uses a single self-rest ADC(SR-ADC) with low sample rate, and it achieves large dynamic range and ultra-wideband receiving simultaneously. Two receiving scenarios are considered, and they are cooperative strong signal receiving and non-cooperative strong/weak signals receiving. In the cooperative receiving scenario, an improved fast recovery method is proposed to obtain the modulated sampling output. In the non-cooperative receiving scenario, the strong and weak signals with different carrier frequencies are considered, and the signal processing method can recover and estimate each signal. Simulation results show that the proposed scheme can realize large dynamic range and ultra-wideband receiving simultaneously when the input signal-to-noise(SNR) ratio is high.
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 Agence Nationale de la Recherche under grant ANR-08-BLAN-0294-02
文摘A convex variational formulation is proposed to solve multicomponent signal processing problems in Hilbert spaces.The cost function consists of a separable term, in which each component is modeled through its own potential,and of a coupling term, in which constraints on linear transformations of the components are penalized with smooth functionals.An algorithm with guaranteed weak convergence to a solution to the problem is provided.Various multicomponent signal decomposition and recovery applications are discussed.
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The National Basic Research Program of China(973 program)(No.2011CB707904)the National Natural Science Foundation of China(No.61073138,61271312,61201344,81101104,60911130370)+1 种基金the Research Fund for the Doctoral Program of Higher Education of Ministry of Education of China(No.20110092110023,20120092120036)the Natural Science Foundation of Jiangsu Province(No.BK2012329,BK2012743)
文摘An algorithm for recovering the quaternion signals in both noiseless and noise contaminated scenarios by solving an L1-norm minimization problem is presented. The L1-norm minimization problem over the quaternion number field is solved by converting it to an equivalent second-order cone programming problem over the real number field, which can be readily solved by convex optimization solvers like SeDuMi. Numerical experiments are provided to illustrate the effectiveness of the proposed algorithm. In a noiseless scenario, the experimental results show that under some practically acceptable conditions, exact signal recovery can be achieved. With additive noise contamination in measurements, the experimental results show that the proposed algorithm is robust to noise. The proposed algorithm can be applied in compressed-sensing-based signal recovery in the quaternion domain.
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.
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 NSF of China(Grant Nos.12271050,11871109,11901037)by the CAEP Foundation(Grant No.CX20200027)by the Key Laboratory of Computational Physics Foundation(Grant No.6142A05210502).
文摘This paper considers a corrupted compressed sensing problem and is devoted to recover signals that are approximately sparse in some general dictionary but corrupted by a combination of interference having a sparse representation in a second general dictionary and measurement noise.We provide new restricted isometry property(RIP)analysis to achieve stable recovery of sparsely corrupted signals through Justice Pursuit De-Noising(JPDN)with an additional parameter.Our main tool is to adapt a crucial sparse decomposition technique to the analysis of the Justice Pursuit method.The proposed RIP condition improves the existing representative results.Numerical simulations are provided to verify the reliability of the JPDN model.
文摘Aiming at the problem that the positioning accuracy of WiFi indoor positioning technology based on location fingerprint has not reached the requirements of practical application, a WiFi indoor positioning and tracking algorithm combining adaptive affine propagation (AAPC), compressed sensing (CS) and Kalman filter is proposed. In the off-line phase, AAPC algorithm is used to generate clustering fingerprints with optimal clustering effect performance;In the online phase, CS and nearest neighbor algorithm are used for position estimation;Finally, the Kalman filter and physical constraints are combined to perform positioning and tracking. By collecting a large number of real experimental data, it is proved that the developed algorithm has higher positioning accuracy and more accurate trajectory tracking effect.
基金This work was supported by the National Natural Science Foundation of China(61871146).
文摘This paper concentrates on super-resolution imaging of the ship target under the sparse aperture situation.Firstly,a multi-static configuration is utilized to solve the coherent processing interval(CPI)problem caused by the slow-speed motion of ship targets.Then,we realize signal restoration and image reconstruction with the alternating direction method of multipliers(ADMM).Furthermore,we adopt the interferometric technique to produce the three-dimensional(3D)images of ship targets,namely interferometric inverse synthetic aperture radar(InISAR)imaging.Experiments based on the simulated data are utilized to verify the validity of the proposed method.
基金supported by National Science Foundation of USA(Grant Nos.DMS-1403400 and DMS-1712602)National Natural Science Foundation of China(Grant Nos.11171151,11371200,11525104 and 11531013)
文摘In an earlier work, we proposed a frame-based kernel analysis approach to the problem of recovering erasures from unknown locations. The new approach led to the stability question on recovering a signal from noisy partial frame coefficients with erasures occurring at unknown locations. In this continuing work, we settle this problem by obtaining a complete characterization of frames that provide stable reconstructions. We show that an encoding frame provides a stable signal recovery from noisy partial frame coefficients at unknown locations if and only if it is totally robust with respect to erasures. We present several characterizations for either totally robust frames or almost robust frames. Based on these characterizations several explicit construction algorithms for totally robust and almost robust frames are proposed. As a consequence of the construction methods, we obtain that the probability for a randomly generated frame to be totally robust with respect to a fixed number of erasures is one.
