Broadband wireless channels are often time dispersive and become strongly frequency selective in delay spread domain. Commonly, these channels are composed of a few dominant coefficients and a large part of coefficien...Broadband wireless channels are often time dispersive and become strongly frequency selective in delay spread domain. Commonly, these channels are composed of a few dominant coefficients and a large part of coefficients are approximately zero or under noise floor. To exploit sparsity of multi-path channels (MPCs), there are various methods have been proposed. They are, namely, greedy algorithms, iterative algorithms, and convex program. The former two algorithms are easy to be implemented but not stable;on the other hand, the last method is stable but difficult to be implemented as practical channel estimation problems be-cause of computational complexity. In this paper, we introduce a novel channel estimation strategy using smooth L0 (SL0) algorithm which combines stable and low complexity. Computer simulations confirm the effectiveness of the introduced algorithm. We also give various simulations to verify the sensing training signal method.展开更多
l_(0)梯度最小化图像平滑算法可在保持边缘的同时滤除纹理和细节,但该算法使用图像梯度判决被平滑成分时会出现包含较小图像梯度(弱边缘)的区域会被平滑,而包含较大图像梯度(强纹理)的区域被保留的现象.为克服此缺陷,提出一种基于图像块...l_(0)梯度最小化图像平滑算法可在保持边缘的同时滤除纹理和细节,但该算法使用图像梯度判决被平滑成分时会出现包含较小图像梯度(弱边缘)的区域会被平滑,而包含较大图像梯度(强纹理)的区域被保留的现象.为克服此缺陷,提出一种基于图像块l_(0)梯度最小化算法(image-patch based l_(0)gradient minimization algorithm,简称IP-l_(0)算法)的图像平滑算法,通过对输入图像中的图像块而非整幅图像进行平滑,动态改变图像块目标函数中的权重参数,令主要包含强纹理的图像块以较大的力度进行平滑,而主要包含弱边缘的图像块以较小的力度进行平滑,再整合平滑后的图像块得到整个边缘保持平滑图像.对IP-l_(0)算法、原始的l_(0)梯度最小化算法、基于局部拉普拉斯滤波器的算法、基于相对全变差算法、基于树滤波的算法,以及2种基于深度学习的边缘保持算法进行仿真实验,结果表明,使用IP-l_(0)算法滤波后的图像能在保持较弱的边缘的同时平滑强纹理.展开更多
We consider the solutions of refinement equations written in the form$$\varphi \left( x \right) = \sum\limits_{\alpha \in \Zopf^s} {a\left( \alpha \right)\varphi \left( {Mx - \alpha } \right) + g\left( x \right),\,\,\...We consider the solutions of refinement equations written in the form$$\varphi \left( x \right) = \sum\limits_{\alpha \in \Zopf^s} {a\left( \alpha \right)\varphi \left( {Mx - \alpha } \right) + g\left( x \right),\,\,\,x \in \Ropf^s} $$where the vector of functions } = (}1, ..., }r)T is unknown, g is a given vector of compactly supported functions on A^s, a is a finitely supported sequence of r 2 r matrices called the refinement mask, and M is an s 2 s dilation matrix with m = |detM|. Inhomogeneous refinement equations appear in the construction of multiwavelets and the constructions of wavelets on a finite interval. The cascade algorithm with mask a, g, and dilation M generates a sequence }n, n = 1, 2, ..., by the iterative process$$\varphi _n \left( x \right) = \sum\limits_{\alpha \in \Zopf^s} {a\left( \alpha \right)\varphi _{n - 1} \left(Mx - \alpha \right) + g\left( x \right),\,\,\,x \in \Ropf^s} $$from a starting vector of function }0. We characterize the Lp-convergence (0 < p < 1) of the cascade algorithm in terms of the p-norm joint spectral radius of a collection of linear operators associated with the refinement mask. We also obtain a smoothness property of the solutions of the refinement equations associated with the homogeneous refinement equation.展开更多
The sparse recovery algorithms formulate synthetic aperture radar （SAR） imaging problem in terms of sparse representation （SR） of a small number of strong scatters＇ positions among a much large number of potentia...The sparse recovery algorithms formulate synthetic aperture radar （SAR） imaging problem in terms of sparse representation （SR） of a small number of strong scatters＇ positions among a much large number of potential scatters＇ positions, and provide an effective approach to improve the SAR image resolution. Based on the attributed scatter center model, several experiments were performed with different practical considerations to evaluate the performance of five representative SR techniques, namely, sparse Bayesian learning （SBL）, fast Bayesian matching pursuit （FBMP）, smoothed 10 norm method （SL0）, sparse reconstruction by separable approximation （SpaRSA）, fast iterative shrinkage-thresholding algorithm （FISTA）, and the parameter settings in five SR algorithms were discussed. In different situations, the performances of these algorithms were also discussed. Through the comparison of MSE and failure rate in each algorithm simulation, FBMP and SpaRSA are found suitable for dealing with problems in the SAR imaging based on attributed scattering center model. Although the SBL is time-consuming, it always get better performance when related to failure rate and high SNR.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
文摘Broadband wireless channels are often time dispersive and become strongly frequency selective in delay spread domain. Commonly, these channels are composed of a few dominant coefficients and a large part of coefficients are approximately zero or under noise floor. To exploit sparsity of multi-path channels (MPCs), there are various methods have been proposed. They are, namely, greedy algorithms, iterative algorithms, and convex program. The former two algorithms are easy to be implemented but not stable;on the other hand, the last method is stable but difficult to be implemented as practical channel estimation problems be-cause of computational complexity. In this paper, we introduce a novel channel estimation strategy using smooth L0 (SL0) algorithm which combines stable and low complexity. Computer simulations confirm the effectiveness of the introduced algorithm. We also give various simulations to verify the sensing training signal method.
文摘l_(0)梯度最小化图像平滑算法可在保持边缘的同时滤除纹理和细节,但该算法使用图像梯度判决被平滑成分时会出现包含较小图像梯度(弱边缘)的区域会被平滑,而包含较大图像梯度(强纹理)的区域被保留的现象.为克服此缺陷,提出一种基于图像块l_(0)梯度最小化算法(image-patch based l_(0)gradient minimization algorithm,简称IP-l_(0)算法)的图像平滑算法,通过对输入图像中的图像块而非整幅图像进行平滑,动态改变图像块目标函数中的权重参数,令主要包含强纹理的图像块以较大的力度进行平滑,而主要包含弱边缘的图像块以较小的力度进行平滑,再整合平滑后的图像块得到整个边缘保持平滑图像.对IP-l_(0)算法、原始的l_(0)梯度最小化算法、基于局部拉普拉斯滤波器的算法、基于相对全变差算法、基于树滤波的算法,以及2种基于深度学习的边缘保持算法进行仿真实验,结果表明,使用IP-l_(0)算法滤波后的图像能在保持较弱的边缘的同时平滑强纹理.
基金supported by NSF of China under Grant No.10071071
文摘We consider the solutions of refinement equations written in the form$$\varphi \left( x \right) = \sum\limits_{\alpha \in \Zopf^s} {a\left( \alpha \right)\varphi \left( {Mx - \alpha } \right) + g\left( x \right),\,\,\,x \in \Ropf^s} $$where the vector of functions } = (}1, ..., }r)T is unknown, g is a given vector of compactly supported functions on A^s, a is a finitely supported sequence of r 2 r matrices called the refinement mask, and M is an s 2 s dilation matrix with m = |detM|. Inhomogeneous refinement equations appear in the construction of multiwavelets and the constructions of wavelets on a finite interval. The cascade algorithm with mask a, g, and dilation M generates a sequence }n, n = 1, 2, ..., by the iterative process$$\varphi _n \left( x \right) = \sum\limits_{\alpha \in \Zopf^s} {a\left( \alpha \right)\varphi _{n - 1} \left(Mx - \alpha \right) + g\left( x \right),\,\,\,x \in \Ropf^s} $$from a starting vector of function }0. We characterize the Lp-convergence (0 < p < 1) of the cascade algorithm in terms of the p-norm joint spectral radius of a collection of linear operators associated with the refinement mask. We also obtain a smoothness property of the solutions of the refinement equations associated with the homogeneous refinement equation.
基金Project(61171133)supported by the National Natural Science Foundation of ChinaProject(11JJ1010)supported by the Natural Science Fund for Distinguished Young Scholars of Hunan Province,ChinaProject(61101182)supported by National Natural Science Foundation for Young Scientists of China
文摘The sparse recovery algorithms formulate synthetic aperture radar （SAR） imaging problem in terms of sparse representation （SR） of a small number of strong scatters＇ positions among a much large number of potential scatters＇ positions, and provide an effective approach to improve the SAR image resolution. Based on the attributed scatter center model, several experiments were performed with different practical considerations to evaluate the performance of five representative SR techniques, namely, sparse Bayesian learning （SBL）, fast Bayesian matching pursuit （FBMP）, smoothed 10 norm method （SL0）, sparse reconstruction by separable approximation （SpaRSA）, fast iterative shrinkage-thresholding algorithm （FISTA）, and the parameter settings in five SR algorithms were discussed. In different situations, the performances of these algorithms were also discussed. Through the comparison of MSE and failure rate in each algorithm simulation, FBMP and SpaRSA are found suitable for dealing with problems in the SAR imaging based on attributed scattering center model. Although the SBL is time-consuming, it always get better performance when related to failure rate and high SNR.
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.
