In this paper,we propose a variable metric extrapolation proximal iterative hard thresholding(VMEPIHT)method for nonconvex\ell_0-norm sparsity regularization problem which has wide applications in signal and image pro...In this paper,we propose a variable metric extrapolation proximal iterative hard thresholding(VMEPIHT)method for nonconvex\ell_0-norm sparsity regularization problem which has wide applications in signal and image processing,machine learning and so on.The VMEPIHT method is based on the forward-backward splitting(FBS)method,and variable metric strategy is employed in the extrapolation step to speed up the algorithm.The proposed method’s convergence,linear convergence rate and superlinear convergence rate are shown under appropriate assumptions.Finally,we conduct numerical experiments on compressed sensing problem and CT image reconstruction problem to confirm the efficiency of the proposed method,compared with other state-of-the-art methods.展开更多
The iterative hard thresholding(IHT)algorithm is a powerful and efficient algorithm for solving l_(0)-regularized problems and inspired many applications in sparse-approximation and image-processing fields.Recently,so...The iterative hard thresholding(IHT)algorithm is a powerful and efficient algorithm for solving l_(0)-regularized problems and inspired many applications in sparse-approximation and image-processing fields.Recently,some convergence results are established for the proximal scheme of IHT,namely proximal iterative hard thresholding(PIHT)algorithm(Blumensath and Davies,in J Fourier Anal Appl 14:629–654,2008;Hu et al.,Methods 67:294–303,2015;Lu,Math Program 147:125–154,2014;Trzasko et al.,IEEE/SP 14th Workshop on Statistical Signal Processing,2007)on solving the related l_(0)-optimization problems.However,the complexity analysis for the PIHT algorithm is not well explored.In this paper,we aim to provide some complexity estimations for the PIHT sequences.In particular,we show that the complexity of the sequential iterate error is at o(1/k).Under the assumption that the objective function is composed of a quadratic convex function and l_(0)regularization,we show that the PIHT algorithm has R-linear convergence rate.Finally,we illustrate some applications of this algorithm for compressive sensing reconstruction and sparse learning and validate the estimated error bounds.展开更多
针对互耦效应和脉冲噪声并存环境下的波达方向(direction of arrival,DOA)估计问题,提出一种结合M估计与稀疏重构的算法。首先,为了消除互耦效应的影响,依据互耦矩阵的托普利兹结构进行恒等变形,得到了不含未知互耦系数的字典。随后,为...针对互耦效应和脉冲噪声并存环境下的波达方向(direction of arrival,DOA)估计问题,提出一种结合M估计与稀疏重构的算法。首先,为了消除互耦效应的影响,依据互耦矩阵的托普利兹结构进行恒等变形,得到了不含未知互耦系数的字典。随后,为了使算法能适应高斯噪声和不同强度的脉冲噪声,将位置得分函数表示为高斯位置得分函数和一系列非线性函数的线性组合,利用噪声样本估计线性组合系数从而建立损失函数。最后,采用迭代硬阈值算法进行稀疏重构,并通过改进信号更新策略提高正确收敛的概率。仿真结果表明,所提算法能有效抑制互耦效应和脉冲(高斯)噪声的干扰,同时相较已有算法在低信噪比、强脉冲特性下的性能有显著提升。展开更多
Missing data are a problem in geophysical surveys, and interpolation and reconstruction of missing data is part of the data processing and interpretation. Based on the sparseness of the geophysical data or the transfo...Missing data are a problem in geophysical surveys, and interpolation and reconstruction of missing data is part of the data processing and interpretation. Based on the sparseness of the geophysical data or the transform domain, we can improve the accuracy and stability of the reconstruction by transforming it to a sparse optimization problem. In this paper, we propose a mathematical model for the sparse reconstruction of data based on the LO-norm minimization. Furthermore, we discuss two types of the approximation algorithm for the LO- norm minimization according to the size and characteristics of the geophysical data： namely, the iteratively reweighted least-squares algorithm and the fast iterative hard thresholding algorithm. Theoretical and numerical analysis showed that applying the iteratively reweighted least-squares algorithm to the reconstruction of potential field data exploits its fast convergence rate, short calculation time, and high precision, whereas the fast iterative hard thresholding algorithm is more suitable for processing seismic data, moreover, its computational efficiency is better than that of the traditional iterative hard thresholding algorithm.展开更多
针对压缩传感(Compressed sensing,CS)理论中迭代硬阈值(Iterative hard thresholding,IHT)算法迭代次数多和时间长的问题,提出基于回溯的迭代硬阈值算法(Backtracking-based iterative hard thresholding,BIHT),该算法通过加入回溯的思...针对压缩传感(Compressed sensing,CS)理论中迭代硬阈值(Iterative hard thresholding,IHT)算法迭代次数多和时间长的问题,提出基于回溯的迭代硬阈值算法(Backtracking-based iterative hard thresholding,BIHT),该算法通过加入回溯的思想,优化了IHT算法迭代支撑的选择,减少支撑被反复选择的次数.模拟实验表明,在保证重建质量的前提下,相比较于IHT和正规化迭代硬阈值(Normalized IHT,NIHT)算法,BIHT算法的重建时间降低了2个数量级.用本身稀疏的0-1随机信号的重建实验表明,若测量次数和稀疏度相同,BIHT算法的重建概率高于IHT算法.展开更多
基金supported by the National Natural Science Foundation of China(No.11901368).
文摘In this paper,we propose a variable metric extrapolation proximal iterative hard thresholding(VMEPIHT)method for nonconvex\ell_0-norm sparsity regularization problem which has wide applications in signal and image processing,machine learning and so on.The VMEPIHT method is based on the forward-backward splitting(FBS)method,and variable metric strategy is employed in the extrapolation step to speed up the algorithm.The proposed method’s convergence,linear convergence rate and superlinear convergence rate are shown under appropriate assumptions.Finally,we conduct numerical experiments on compressed sensing problem and CT image reconstruction problem to confirm the efficiency of the proposed method,compared with other state-of-the-art methods.
基金supported by the National Natural Science Foundation of China(No.91330102)973 program(No.2015CB856000).
文摘The iterative hard thresholding(IHT)algorithm is a powerful and efficient algorithm for solving l_(0)-regularized problems and inspired many applications in sparse-approximation and image-processing fields.Recently,some convergence results are established for the proximal scheme of IHT,namely proximal iterative hard thresholding(PIHT)algorithm(Blumensath and Davies,in J Fourier Anal Appl 14:629–654,2008;Hu et al.,Methods 67:294–303,2015;Lu,Math Program 147:125–154,2014;Trzasko et al.,IEEE/SP 14th Workshop on Statistical Signal Processing,2007)on solving the related l_(0)-optimization problems.However,the complexity analysis for the PIHT algorithm is not well explored.In this paper,we aim to provide some complexity estimations for the PIHT sequences.In particular,we show that the complexity of the sequential iterate error is at o(1/k).Under the assumption that the objective function is composed of a quadratic convex function and l_(0)regularization,we show that the PIHT algorithm has R-linear convergence rate.Finally,we illustrate some applications of this algorithm for compressive sensing reconstruction and sparse learning and validate the estimated error bounds.
文摘针对互耦效应和脉冲噪声并存环境下的波达方向(direction of arrival,DOA)估计问题,提出一种结合M估计与稀疏重构的算法。首先,为了消除互耦效应的影响,依据互耦矩阵的托普利兹结构进行恒等变形,得到了不含未知互耦系数的字典。随后,为了使算法能适应高斯噪声和不同强度的脉冲噪声,将位置得分函数表示为高斯位置得分函数和一系列非线性函数的线性组合,利用噪声样本估计线性组合系数从而建立损失函数。最后,采用迭代硬阈值算法进行稀疏重构,并通过改进信号更新策略提高正确收敛的概率。仿真结果表明,所提算法能有效抑制互耦效应和脉冲(高斯)噪声的干扰,同时相较已有算法在低信噪比、强脉冲特性下的性能有显著提升。
基金supported by the National Natural Science Foundation of China (Grant No.41074133)
文摘Missing data are a problem in geophysical surveys, and interpolation and reconstruction of missing data is part of the data processing and interpretation. Based on the sparseness of the geophysical data or the transform domain, we can improve the accuracy and stability of the reconstruction by transforming it to a sparse optimization problem. In this paper, we propose a mathematical model for the sparse reconstruction of data based on the LO-norm minimization. Furthermore, we discuss two types of the approximation algorithm for the LO- norm minimization according to the size and characteristics of the geophysical data： namely, the iteratively reweighted least-squares algorithm and the fast iterative hard thresholding algorithm. Theoretical and numerical analysis showed that applying the iteratively reweighted least-squares algorithm to the reconstruction of potential field data exploits its fast convergence rate, short calculation time, and high precision, whereas the fast iterative hard thresholding algorithm is more suitable for processing seismic data, moreover, its computational efficiency is better than that of the traditional iterative hard thresholding algorithm.
文摘针对压缩传感(Compressed sensing,CS)理论中迭代硬阈值(Iterative hard thresholding,IHT)算法迭代次数多和时间长的问题,提出基于回溯的迭代硬阈值算法(Backtracking-based iterative hard thresholding,BIHT),该算法通过加入回溯的思想,优化了IHT算法迭代支撑的选择,减少支撑被反复选择的次数.模拟实验表明,在保证重建质量的前提下,相比较于IHT和正规化迭代硬阈值(Normalized IHT,NIHT)算法,BIHT算法的重建时间降低了2个数量级.用本身稀疏的0-1随机信号的重建实验表明,若测量次数和稀疏度相同,BIHT算法的重建概率高于IHT算法.
