Block multiple measurement vectors (BMMV) is a reconstruction algorithm that can be used to recover the support of block K-joint sparse matrix X from Y = ΨX + V. In this paper, we propose a sufficient condition for a...Block multiple measurement vectors (BMMV) is a reconstruction algorithm that can be used to recover the support of block K-joint sparse matrix X from Y = ΨX + V. In this paper, we propose a sufficient condition for accurate support recovery of the block K-joint sparse matrix via the BMMV algorithm in the noisy case. Furthermore, we show the optimality of the condition we proposed in the absence of noise when the problem reduces to single measurement vector case.展开更多
Several problems in imaging acquire multiple measurement vectors(MMVs)of Fourier samples for the same underlying scene.Image recovery techniques from MMVs aim to exploit the joint sparsity across the measurements in t...Several problems in imaging acquire multiple measurement vectors(MMVs)of Fourier samples for the same underlying scene.Image recovery techniques from MMVs aim to exploit the joint sparsity across the measurements in the sparse domain.This is typically accomplished by extending the use of`1 regularization of the sparse domain in the single measurement vector(SMV)case to using`2,1 regularization so that the“jointness”can be accounted for.Although effective,the approach is inherently coupled and therefore computationally inefficient.The method also does not consider current approaches in the SMV case that use spatially varying weighted`1 regularization term.The recently introduced variance based joint sparsity(VBJS)recovery method uses the variance across the measurements in the sparse domain to produce a weighted MMV method that is more accurate and more efficient than the standard`2,1 approach.The efficiency is due to the decoupling of the measurement vectors,with the increased accuracy resulting from the spatially varying weight.Motivated by these results,this paper introduces a new technique to even further reduce computational cost by eliminating the requirement to first approximate the underlying image in order to construct the weights.Eliminating this preprocessing step moreover reduces the amount of information lost from the data,so that our method is more accurate.Numerical examples provided in the paper verify these benefits.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
文摘Block multiple measurement vectors (BMMV) is a reconstruction algorithm that can be used to recover the support of block K-joint sparse matrix X from Y = ΨX + V. In this paper, we propose a sufficient condition for accurate support recovery of the block K-joint sparse matrix via the BMMV algorithm in the noisy case. Furthermore, we show the optimality of the condition we proposed in the absence of noise when the problem reduces to single measurement vector case.
文摘Several problems in imaging acquire multiple measurement vectors(MMVs)of Fourier samples for the same underlying scene.Image recovery techniques from MMVs aim to exploit the joint sparsity across the measurements in the sparse domain.This is typically accomplished by extending the use of`1 regularization of the sparse domain in the single measurement vector(SMV)case to using`2,1 regularization so that the“jointness”can be accounted for.Although effective,the approach is inherently coupled and therefore computationally inefficient.The method also does not consider current approaches in the SMV case that use spatially varying weighted`1 regularization term.The recently introduced variance based joint sparsity(VBJS)recovery method uses the variance across the measurements in the sparse domain to produce a weighted MMV method that is more accurate and more efficient than the standard`2,1 approach.The efficiency is due to the decoupling of the measurement vectors,with the increased accuracy resulting from the spatially varying weight.Motivated by these results,this paper introduces a new technique to even further reduce computational cost by eliminating the requirement to first approximate the underlying image in order to construct the weights.Eliminating this preprocessing step moreover reduces the amount of information lost from the data,so that our method is more accurate.Numerical examples provided in the paper verify these benefits.
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.
