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
In some applications, there are signals with piecewise structure to be recovered. In this paper, we propose a piecewise OMP（P OMP） method which aims to preserve the piecewise sparse structure（or the small-scaled en...In some applications, there are signals with piecewise structure to be recovered. In this paper, we propose a piecewise OMP（P OMP） method which aims to preserve the piecewise sparse structure（or the small-scaled entries） of piecewise signals. Besides the merits of OMP,the P OMP, which is a generalization of the combination of CoSaMP and OMMP（Orthogonal Multi-matching Pursuit） on piecewise sparse recovery, possesses the advantages of comparable approximation error decay as CoSaMP with more relaxed sufficient condition and better recovery success rate. Moreover, the P OMP algorithm recovers the piecewise sparse signal according to its piecewise structure, which results in better details preservation. Numerical experiments indicate that compared with CoSaMP, OMP, OMMP and BP methods, the P OMP algorithm is more effective and robust for piecewise sparse recovery.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 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
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(Grant Nos.11471066 11572081+1 种基金 11871137)the Fundamental Research Funds for the Central Universities(Grant No.QYWKC2018007)
文摘In some applications, there are signals with piecewise structure to be recovered. In this paper, we propose a piecewise OMP（P OMP） method which aims to preserve the piecewise sparse structure（or the small-scaled entries） of piecewise signals. Besides the merits of OMP,the P OMP, which is a generalization of the combination of CoSaMP and OMMP（Orthogonal Multi-matching Pursuit） on piecewise sparse recovery, possesses the advantages of comparable approximation error decay as CoSaMP with more relaxed sufficient condition and better recovery success rate. Moreover, the P OMP algorithm recovers the piecewise sparse signal according to its piecewise structure, which results in better details preservation. Numerical experiments indicate that compared with CoSaMP, OMP, OMMP and BP methods, the P OMP algorithm is more effective and robust for piecewise sparse recovery.
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.
