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 the multi-target localization based on Compressed Sensing(CS),the sensing matrix's characteristic is significant to the localization accuracy.To improve the CS-based localization approach's performance,we p...In the multi-target localization based on Compressed Sensing(CS),the sensing matrix's characteristic is significant to the localization accuracy.To improve the CS-based localization approach's performance,we propose a sensing matrix optimization method in this paper,which considers the optimization under the guidance of the t%-averaged mutual coherence.First,we study sensing matrix optimization and model it as a constrained combinatorial optimization problem.Second,the t%-averaged mutual coherence is adopted as the optimality index to evaluate the quality of different sensing matrixes,where the threshold t is derived through the K-means clustering.With the settled optimality index,a hybrid metaheuristic algorithm named Genetic Algorithm-Tabu Local Search(GA-TLS)is proposed to address the combinatorial optimization problem to obtain the final optimized sensing matrix.Extensive simulation results reveal that the CS localization approaches using different recovery algorithms benefit from the proposed sensing matrix optimization method,with much less localization error compared to the traditional sensing matrix optimization methods.展开更多
Compressed Sensing （CS） offers a method to solve the channel estimation problems for an underwater acoustic system, based on the existence of a sparse representation of the treated signal and an overcomplete diction...Compressed Sensing （CS） offers a method to solve the channel estimation problems for an underwater acoustic system, based on the existence of a sparse representation of the treated signal and an overcomplete dictionary with a set of non-orthogonal bases. In this paper, we proposed a new approach to optimize dictionaries by decreasing the average measure of the mutual coherence of the effective dictionary. A fixed link between the average mutual coherence and the CS perforrmnce is indicated by designing three factors： operating bandwidth, the number of pilot subcarriers, and coherence bandwidth. Both the Orthogonal Matching Pursuit （OMP） and the Basis Pursuit De-Noising （BPDN） are compared to the Dantzig Selector （DS） for different Signal Noise Ratio （SNR） and shown to benefit from the newly designed dictionary. Nurnerical sinmlations and experimental data of an OFDM receiver are used to evaluate the proposed method in comparison with the conventional LeastSquare （LS） estirmtor. The results show that the dictionary with a better condition considerably improves the perforrmnce of the channel estimation.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
Sustained mutual coherence between 2 combs over extended periods is a prerequisite for dual-comb spectroscopy(DCS),particularly in achieving high-resolution molecular spectroscopy and precise spectral measurements.How...Sustained mutual coherence between 2 combs over extended periods is a prerequisite for dual-comb spectroscopy(DCS),particularly in achieving high-resolution molecular spectroscopy and precise spectral measurements.However,achieving long coherence times remains a challenge for Yb-doped frequency combs.This work introduces an experimental approach for phase-stable DCS using Yb-doped frequency combs at 1.03μm with a novel feed-forward method,combatting the limitations of mutual coherence.Without relying on postprocessing or self-correction algorithms,we achieve a coherence time of 1,000 s-3 orders of magnitude longer than the current state of the art for DCS.This extended coherence enables time-domain averaging,resulting in a signal-to-noise ratio(SNR)of 2,045.We demonstrate high-resolution monitoring of weak overtone transitions in the P and R branches of C_(2)H_(2),achieving good agreement with simulated spectra based on HITRAN parameters.The phase-locked multiheterodyne system also enables phase spectrum measurements with a scatter down to 7 mrad.Furthermore,we successfully extend our technique to the visible spectral region using second harmonic generation,achieving high-resolution spectra of NO_(2)with excellent SNR.The method offers high-frequency accuracy and demonstrates the potential of Yb-doped systems for multiplexed metrology,effectively extending the capabilities of DCS as a powerful tool for multi-disciplinary applications.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
The extended Huygens-Fresnel principle and Goodman model was utilized for target surface to derive the mutual coherence function(MCF) of a Gaussian beam reflected from an arbitrary rough target in atmospheric turbulen...The extended Huygens-Fresnel principle and Goodman model was utilized for target surface to derive the mutual coherence function(MCF) of a Gaussian beam reflected from an arbitrary rough target in atmospheric turbulence. According to the MCF, expressions of the mean irradiance and average speckle size at the receiver were obtained. The analysis indicated that the mean intensity is closely related to the ratio of root mean square(rms) height to the lateral correlation length. In addition, the speckle size at the receiver is associated with turbulence strength, propagation distance and roughness of the target. The results can be reduced to the result of a Gaussian beam illuminating rough target and scattering from a target in free space.展开更多
In this paper,we propose a Quasi-Orthogonal Matching Pursuit(QOMP)algorithm for constructing a sparse approximation of functions in terms of expansion by orthonormal polynomials.For the two kinds of sampled data,data ...In this paper,we propose a Quasi-Orthogonal Matching Pursuit(QOMP)algorithm for constructing a sparse approximation of functions in terms of expansion by orthonormal polynomials.For the two kinds of sampled data,data with noises and without noises,we apply the mutual coherence of measurement matrix to establish the convergence of the QOMP algorithm which can reconstruct s-sparse Legendre polynomials,Chebyshev polynomials and trigonometric polynomials in s step iterations.The results are also extended to general bounded orthogonal system including tensor product of these three univariate orthogonal polynomials.Finally,numerical experiments will be presented to verify the effectiveness of the QOMP method.展开更多
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In the multi-target localization based on Compressed Sensing(CS),the sensing matrix's characteristic is significant to the localization accuracy.To improve the CS-based localization approach's performance,we propose a sensing matrix optimization method in this paper,which considers the optimization under the guidance of the t%-averaged mutual coherence.First,we study sensing matrix optimization and model it as a constrained combinatorial optimization problem.Second,the t%-averaged mutual coherence is adopted as the optimality index to evaluate the quality of different sensing matrixes,where the threshold t is derived through the K-means clustering.With the settled optimality index,a hybrid metaheuristic algorithm named Genetic Algorithm-Tabu Local Search(GA-TLS)is proposed to address the combinatorial optimization problem to obtain the final optimized sensing matrix.Extensive simulation results reveal that the CS localization approaches using different recovery algorithms benefit from the proposed sensing matrix optimization method,with much less localization error compared to the traditional sensing matrix optimization methods.
基金Acknowledgements This work was supported by the National Science Foundation of China under Grant No. 60976065. The authors would like to thank the anonymous reviewers for comments that helped improve the paper.
文摘Compressed Sensing （CS） offers a method to solve the channel estimation problems for an underwater acoustic system, based on the existence of a sparse representation of the treated signal and an overcomplete dictionary with a set of non-orthogonal bases. In this paper, we proposed a new approach to optimize dictionaries by decreasing the average measure of the mutual coherence of the effective dictionary. A fixed link between the average mutual coherence and the CS perforrmnce is indicated by designing three factors： operating bandwidth, the number of pilot subcarriers, and coherence bandwidth. Both the Orthogonal Matching Pursuit （OMP） and the Basis Pursuit De-Noising （BPDN） are compared to the Dantzig Selector （DS） for different Signal Noise Ratio （SNR） and shown to benefit from the newly designed dictionary. Nurnerical sinmlations and experimental data of an OFDM receiver are used to evaluate the proposed method in comparison with the conventional LeastSquare （LS） estirmtor. The results show that the dictionary with a better condition considerably improves the perforrmnce of the channel estimation.
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 HORIZON EUROPE European Research Council(947288)Austrian Science Fund(FWF)(Y1254)funding from the European Union(grant agreement 101076933 EUVORAM).
文摘Sustained mutual coherence between 2 combs over extended periods is a prerequisite for dual-comb spectroscopy(DCS),particularly in achieving high-resolution molecular spectroscopy and precise spectral measurements.However,achieving long coherence times remains a challenge for Yb-doped frequency combs.This work introduces an experimental approach for phase-stable DCS using Yb-doped frequency combs at 1.03μm with a novel feed-forward method,combatting the limitations of mutual coherence.Without relying on postprocessing or self-correction algorithms,we achieve a coherence time of 1,000 s-3 orders of magnitude longer than the current state of the art for DCS.This extended coherence enables time-domain averaging,resulting in a signal-to-noise ratio(SNR)of 2,045.We demonstrate high-resolution monitoring of weak overtone transitions in the P and R branches of C_(2)H_(2),achieving good agreement with simulated spectra based on HITRAN parameters.The phase-locked multiheterodyne system also enables phase spectrum measurements with a scatter down to 7 mrad.Furthermore,we successfully extend our technique to the visible spectral region using second harmonic generation,achieving high-resolution spectra of NO_(2)with excellent SNR.The method offers high-frequency accuracy and demonstrates the potential of Yb-doped systems for multiplexed metrology,effectively extending the capabilities of DCS as a powerful tool for multi-disciplinary applications.
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(Grant Nos.61172031,61271110 and 61102018)the New Scientific and Technological Star of Shaanxi Province Funded Project(Grant No.2011KJXX39)the Natural Science Foundation of Shaanxi Province education office,China(Grant No.12Jk0955)
文摘The extended Huygens-Fresnel principle and Goodman model was utilized for target surface to derive the mutual coherence function(MCF) of a Gaussian beam reflected from an arbitrary rough target in atmospheric turbulence. According to the MCF, expressions of the mean irradiance and average speckle size at the receiver were obtained. The analysis indicated that the mean intensity is closely related to the ratio of root mean square(rms) height to the lateral correlation length. In addition, the speckle size at the receiver is associated with turbulence strength, propagation distance and roughness of the target. The results can be reduced to the result of a Gaussian beam illuminating rough target and scattering from a target in free space.
基金supported by National Natural Science Foundation of China no.12071019.
文摘In this paper,we propose a Quasi-Orthogonal Matching Pursuit(QOMP)algorithm for constructing a sparse approximation of functions in terms of expansion by orthonormal polynomials.For the two kinds of sampled data,data with noises and without noises,we apply the mutual coherence of measurement matrix to establish the convergence of the QOMP algorithm which can reconstruct s-sparse Legendre polynomials,Chebyshev polynomials and trigonometric polynomials in s step iterations.The results are also extended to general bounded orthogonal system including tensor product of these three univariate orthogonal polynomials.Finally,numerical experiments will be presented to verify the effectiveness of the QOMP method.
