This paper explores the recovery of block sparse signals in frame-based settings using the l_(2)/l_(q)-synthesis technique(0<q≤1).We propose a new null space property,referred to as block D-NSP_(q),which is based ...This paper explores the recovery of block sparse signals in frame-based settings using the l_(2)/l_(q)-synthesis technique(0<q≤1).We propose a new null space property,referred to as block D-NSP_(q),which is based on the dictionary D.We establish that matrices adhering to the block D-NSP_(q)condition are both necessary and sufficient for the exact recovery of block sparse signals via l_(2)/l_(q)-synthesis.Additionally,this condition is essential for the stable recovery of signals that are block-compressible with respect to D.This D-NSP_(q)property is identified as the first complete condition for successful signal recovery using l_(2)/l_(q)-synthesis.Furthermore,we assess the theoretical efficacy of the l2/lq-synthesis method under conditions of measurement noise.展开更多
In this paper,we reconstruct strongly-decaying block sparse signals by the block generalized orthogonal matching pursuit(BgOMP)algorithm in the l2-bounded noise case.Under some restraints on the minimum magnitude of t...In this paper,we reconstruct strongly-decaying block sparse signals by the block generalized orthogonal matching pursuit(BgOMP)algorithm in the l2-bounded noise case.Under some restraints on the minimum magnitude of the nonzero elements of the strongly-decaying block sparse signal,if the sensing matrix satisfies the the block restricted isometry property(block-RIP),then arbitrary strongly-decaying block sparse signals can be accurately and steadily reconstructed by the BgOMP algorithm in iterations.Furthermore,we conjecture that this condition is sharp.展开更多
For the direction of arrival（DOA） estimation,traditional sparse reconstruction methods for wideband signals usually need many iteration times.For this problem,a new method for two-dimensional wideband signals based ...For the direction of arrival（DOA） estimation,traditional sparse reconstruction methods for wideband signals usually need many iteration times.For this problem,a new method for two-dimensional wideband signals based on block sparse reconstruction is proposed.First,a prolate spheroidal wave function（PSWF） is used to fit the wideband signals,then the block sparse reconstruction technology is employed for DOA estimation.The proposed method uses orthogonalization to choose the matching atoms,ensuring that the residual components correspond to the minimum absolute value.Meanwhile,the vectors obtained by iteration are back-disposed according to the corresponding atomic matching rules,so the extra atoms are abandoned in the course of iteration,and the residual components of current iteration are reduced.Thus the original sparse signals are reconstructed.The proposed method reduces iteration times comparing with the traditional reconstruction methods,and the estimation precision is better than the classical two-sided correlation transformation（TCT）algorithm when the snapshot is small or the signal-to-noise ratio（SNR） is low.展开更多
We consider the block orthogonal multi-matching pursuit(BOMMP) algorithm for the recovery of block sparse signals.A sharp condition is obtained for the exact reconstruction of block K-sparse signals via the BOMMP algo...We consider the block orthogonal multi-matching pursuit(BOMMP) algorithm for the recovery of block sparse signals.A sharp condition is obtained for the exact reconstruction of block K-sparse signals via the BOMMP algorithm in the noiseless case,based on the block restricted isometry constant(block-RIC).Moreover,we show that the sharp condition combining with an extra condition on the minimum l_2 norm of nonzero blocks of block K-sparse signals is sufficient to ensure the BOMMP algorithm selects at least one true block index at each iteration until all true block indices are selected in the noisy case.The significance of the results we obtain in this paper lies in the fact that making explicit use of block sparsity of block sparse signals can achieve better recovery performance than ignoring the additional structure in the problem as being in the conventional sense.展开更多
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 the field of image denoising, deep learning technology holds a dominance. However, the current network model tends to lose fine-grained information with the depth of the network. To address this issue, this paper p...In the field of image denoising, deep learning technology holds a dominance. However, the current network model tends to lose fine-grained information with the depth of the network. To address this issue, this paper proposes a Multi-scale Attention Dilated Residual Image Denoising Network(MADRNet) based on skip connection, which consists of Dense Interval Transmission Block(DTB), Sparse Residual Block(SRB), Dilated Residual Attention Reconstruction Block(DRAB) and Noise Extraction Block(NEB). The DTB enhances the classical dense layer by reducing information redundancy and extracting more accurate feature information. Meanwhile, SRB improves feature information exchange and model generalization through the use of sparse mechanism and skip connection strategy with different expansion factors. The NEB is primarily responsible for extracting and estimating noise. Its output, together with that of the sparse residual module, acts on the DRAB to effectively prevent loss of shallow feature information and improve denoising effect. Furthermore, the DRAB integrates an dilated residual block into an attention mechanism to extract hidden noise information while using residual learning technology to reconstruct clear images. We respectively examined the performance of MADRNet in gray image denoising, color image denoising and real image denoising. The experiment results demonstrate that proposed network outperforms some excellent image denoising network in terms of peak signal-to-noise ratio, structural similarity index measurement and denoising time. The proposed network effectively addresses issues associated with the loss of detail information.展开更多
基金Supported by The Featured Innovation Projects of the General University of Guangdong Province(2023KTSCX096)The Special Projects in Key Areas of Guangdong Province(ZDZX1088)Research Team Project of Guangdong University of Education(2024KYCXTD018)。
文摘This paper explores the recovery of block sparse signals in frame-based settings using the l_(2)/l_(q)-synthesis technique(0<q≤1).We propose a new null space property,referred to as block D-NSP_(q),which is based on the dictionary D.We establish that matrices adhering to the block D-NSP_(q)condition are both necessary and sufficient for the exact recovery of block sparse signals via l_(2)/l_(q)-synthesis.Additionally,this condition is essential for the stable recovery of signals that are block-compressible with respect to D.This D-NSP_(q)property is identified as the first complete condition for successful signal recovery using l_(2)/l_(q)-synthesis.Furthermore,we assess the theoretical efficacy of the l2/lq-synthesis method under conditions of measurement noise.
基金supported by Natural Science Foundation of China(62071262)the K.C.Wong Magna Fund at Ningbo University.
文摘In this paper,we reconstruct strongly-decaying block sparse signals by the block generalized orthogonal matching pursuit(BgOMP)algorithm in the l2-bounded noise case.Under some restraints on the minimum magnitude of the nonzero elements of the strongly-decaying block sparse signal,if the sensing matrix satisfies the the block restricted isometry property(block-RIP),then arbitrary strongly-decaying block sparse signals can be accurately and steadily reconstructed by the BgOMP algorithm in iterations.Furthermore,we conjecture that this condition is sharp.
基金supported by the National Natural Science Foundation of China(6150117661201399)+1 种基金the Education Department of Heilongjiang Province Science and Technology Research Projects(12541638)the Developing Key Laboratory of Sensing Technology and Systems in Cold Region of Heilongjiang Province and Ministry of Education,(Heilongjiang University),P.R.China(P201408)
文摘For the direction of arrival（DOA） estimation,traditional sparse reconstruction methods for wideband signals usually need many iteration times.For this problem,a new method for two-dimensional wideband signals based on block sparse reconstruction is proposed.First,a prolate spheroidal wave function（PSWF） is used to fit the wideband signals,then the block sparse reconstruction technology is employed for DOA estimation.The proposed method uses orthogonalization to choose the matching atoms,ensuring that the residual components correspond to the minimum absolute value.Meanwhile,the vectors obtained by iteration are back-disposed according to the corresponding atomic matching rules,so the extra atoms are abandoned in the course of iteration,and the residual components of current iteration are reduced.Thus the original sparse signals are reconstructed.The proposed method reduces iteration times comparing with the traditional reconstruction methods,and the estimation precision is better than the classical two-sided correlation transformation（TCT）algorithm when the snapshot is small or the signal-to-noise ratio（SNR） is low.
基金National Natural Science Foundation of China(Grant Nos. 11271050 and 11371183)
文摘We consider the block orthogonal multi-matching pursuit(BOMMP) algorithm for the recovery of block sparse signals.A sharp condition is obtained for the exact reconstruction of block K-sparse signals via the BOMMP algorithm in the noiseless case,based on the block restricted isometry constant(block-RIC).Moreover,we show that the sharp condition combining with an extra condition on the minimum l_2 norm of nonzero blocks of block K-sparse signals is sufficient to ensure the BOMMP algorithm selects at least one true block index at each iteration until all true block indices are selected in the noisy case.The significance of the results we obtain in this paper lies in the fact that making explicit use of block sparsity of block sparse signals can achieve better recovery performance than ignoring the additional structure in the problem as being in the conventional sense.
基金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funded by National Nature Science Foundation of China,grant number 61302188。
文摘In the field of image denoising, deep learning technology holds a dominance. However, the current network model tends to lose fine-grained information with the depth of the network. To address this issue, this paper proposes a Multi-scale Attention Dilated Residual Image Denoising Network(MADRNet) based on skip connection, which consists of Dense Interval Transmission Block(DTB), Sparse Residual Block(SRB), Dilated Residual Attention Reconstruction Block(DRAB) and Noise Extraction Block(NEB). The DTB enhances the classical dense layer by reducing information redundancy and extracting more accurate feature information. Meanwhile, SRB improves feature information exchange and model generalization through the use of sparse mechanism and skip connection strategy with different expansion factors. The NEB is primarily responsible for extracting and estimating noise. Its output, together with that of the sparse residual module, acts on the DRAB to effectively prevent loss of shallow feature information and improve denoising effect. Furthermore, the DRAB integrates an dilated residual block into an attention mechanism to extract hidden noise information while using residual learning technology to reconstruct clear images. We respectively examined the performance of MADRNet in gray image denoising, color image denoising and real image denoising. The experiment results demonstrate that proposed network outperforms some excellent image denoising network in terms of peak signal-to-noise ratio, structural similarity index measurement and denoising time. The proposed network effectively addresses issues associated with the loss of detail information.
