目的压缩采样匹配追踪(CoSaMP)算法虽然引入回溯的思想,但其原子选择需要大量的观测值且在稀疏度估计不准确时,会降低信号重构精度,增加重构时间,降低重构效率。为提高CoSaMP算法的重构精度,改善算法的重构性能,提出了一种基于广义逆的...目的压缩采样匹配追踪(CoSaMP)算法虽然引入回溯的思想,但其原子选择需要大量的观测值且在稀疏度估计不准确时,会降低信号重构精度,增加重构时间,降低重构效率。为提高CoSaMP算法的重构精度,改善算法的重构性能,提出了一种基于广义逆的分段迭代匹配追踪(St IMP)算法。方法为保证迭代时挑选原子的精确性和快速性,对观测矩阵广义逆化,降低原子库中原子的相干性;原子更新结合正交匹配追踪(OMP)算法筛选原子的准确性与CoSaMP算法的回溯性,将迭代过程分为两个阶段:第1阶段利用OMP算法迭代K/2次;第2阶段以第1阶段OMP算法迭代所得的残差和原子为输入,并采用CoSaMP算法继续迭代,同时改变原子选择标准,从而精确快速地重构出稀疏信号。结果对于1维的高斯随机信号,无论在不同的稀疏度还是观测值下,相比于OMP、CoSaMP、正则化正交匹配追踪(ROMP)算法和傅里叶类圆环压缩采样匹配追踪(FR-CoSaMP)算法,St IMP算法更加稳健,且具有更高重构成功率;对于2维图像信号,在各个采样率下,St IMP算法的峰值信噪比(PSNR)均高于其他重构算法,在采样率为0.7时,St IMP算法的平均PSNR值比OMP、CoSaMP、ROMP和FR-CoSaMP算法分别高2.14 d B、1.20 d B、3.67 d B和0.90 d B,平均重构时间也较OMP、CoSaMP和FR-CoSaMP算法短。结论提出了一种改进的重构算法,对1维高斯随机信号和2维图像信号均有更好的重构效率和重构效果,与原算法和现有的主流图像重构方法相比,St IMP算法更具高效性和实用性。展开更多
A class of latent ancestral graph for modelling the dependence structure of structural vector autoregressive(VAR)model affected by latent variables is proposed.The graphs are mixed graphs with possibly two kind of edg...A class of latent ancestral graph for modelling the dependence structure of structural vector autoregressive(VAR)model affected by latent variables is proposed.The graphs are mixed graphs with possibly two kind of edges,namely directed and bidirected edges.The vertex set denotes random variables at dif-ferent times.In Gaussian case,the latent ancestral graph leads to a simple parameterization model.A modified iterative conditional fitting algorithm is presented to obtain maximum likelihood esti-mation of the parameters.Furthermore,a log-likelihood criterion is used to select the most appropriate models.Simulations are performed using illustrative examples and results are provided to demonstrate the validity of the methods.展开更多
文摘目的压缩采样匹配追踪(CoSaMP)算法虽然引入回溯的思想,但其原子选择需要大量的观测值且在稀疏度估计不准确时,会降低信号重构精度,增加重构时间,降低重构效率。为提高CoSaMP算法的重构精度,改善算法的重构性能,提出了一种基于广义逆的分段迭代匹配追踪(St IMP)算法。方法为保证迭代时挑选原子的精确性和快速性,对观测矩阵广义逆化,降低原子库中原子的相干性;原子更新结合正交匹配追踪(OMP)算法筛选原子的准确性与CoSaMP算法的回溯性,将迭代过程分为两个阶段:第1阶段利用OMP算法迭代K/2次;第2阶段以第1阶段OMP算法迭代所得的残差和原子为输入,并采用CoSaMP算法继续迭代,同时改变原子选择标准,从而精确快速地重构出稀疏信号。结果对于1维的高斯随机信号,无论在不同的稀疏度还是观测值下,相比于OMP、CoSaMP、正则化正交匹配追踪(ROMP)算法和傅里叶类圆环压缩采样匹配追踪(FR-CoSaMP)算法,St IMP算法更加稳健,且具有更高重构成功率;对于2维图像信号,在各个采样率下,St IMP算法的峰值信噪比(PSNR)均高于其他重构算法,在采样率为0.7时,St IMP算法的平均PSNR值比OMP、CoSaMP、ROMP和FR-CoSaMP算法分别高2.14 d B、1.20 d B、3.67 d B和0.90 d B,平均重构时间也较OMP、CoSaMP和FR-CoSaMP算法短。结论提出了一种改进的重构算法,对1维高斯随机信号和2维图像信号均有更好的重构效率和重构效果,与原算法和现有的主流图像重构方法相比,St IMP算法更具高效性和实用性。
基金supported in part by the National Natural Science Foundation of China(60375003)the Aeronautics and Astronautics Basal Science Foundation of China(03I53059)
文摘A class of latent ancestral graph for modelling the dependence structure of structural vector autoregressive(VAR)model affected by latent variables is proposed.The graphs are mixed graphs with possibly two kind of edges,namely directed and bidirected edges.The vertex set denotes random variables at dif-ferent times.In Gaussian case,the latent ancestral graph leads to a simple parameterization model.A modified iterative conditional fitting algorithm is presented to obtain maximum likelihood esti-mation of the parameters.Furthermore,a log-likelihood criterion is used to select the most appropriate models.Simulations are performed using illustrative examples and results are provided to demonstrate the validity of the methods.
