基于稀疏贝叶斯学习的联合平移不变子空间压缩采样.pdfVIP

Vol. 28 No.5 信号处理 第 28 卷第5 期 2012 年5 月 SIGNAL PROCESSING May 2012 基于稀疏贝叶斯学习的联合平移不 变子空间压缩采样 宋靖张剑云游志刚 (合肥电子工程学院 305 教研室，安徽合肥 23∞37) 摘 要:针对一类特殊的有效核函数(active kemel) 未知的联合平移不变子空间(Union of Shift-Invariant Suhspac田， USI) 信号，构建了一种压缩采样模型，将信号的重构过程看作一个线性回归问题，利用稀疏贝叶斯学习(8阴阳 bayesian leaming , SBL) 算法求得该回归模型中的权值参数的最优估计，根据权值参数向量集的支撑集实现信号 的稀疏重构。理论分析表明，对于自 M个核函数(kernel) 以 T 为周期平移生成的平移不变空间(Shift-Invariant S归C田， SI)，若 M个核函数中至多有K(l.;;K运M12)个且未知哪K 个有效时，本文构建的压缩采样模型最低采 样率能够达到2κIT， 这也是利用稀疏度K所能达到的理论上的最低采样率。仿真结果表明，构建的压缩采样模 型能够布效降低这类信号的采样率。 关键词:联合平移不变子空间;压缩采样;稀疏重构;稀疏贝叶斯学习 中图分类号: TP391 文献标i只码:A 文章编号: 1ω3-0530(2012)。当-0680-06 Compressed Sampling in Union of Shift-Invariant Subspace Based on Sparse Bayesian Learning SONG Jing ZHANG Jian-归n YOU Zhi-gang (Electronic Engin帽吨Institute Lab305 , Anhui Province Hefei 23∞137 ， China) Abstract: For tbe signals in a special union of shift-invariant subspaces (USI) 毗.en 由e active kernel functions are un- known , a concrele compressed sampling 盹:heme is proposed. We re阴rd the pr回咽。f signal reconstruction 嗣 a lin-ear re- gression model and acquire the optional weights by s归rse bayesian learning , then the signal can be recons恤cted accurately k田n 由e support of wei阱t v，配t盯盹t. FOI a continuous-time sparse signal in shift-invariant s阳C回咐uch is genemted by M kernels with period T , however , there are only K out of the M kernels are active 剧td we do not know which K are ch(脚n， we can 国mple 由e signal at 2K1 T mte by 由e sampling scheme ,which is 出nrinimal sarnpling rate 明白 exploiting