基于0-1稀疏循环矩阵的测量矩阵分离研究  

Separation Research of Measurement Matrices Based on 0-1 Sparse Circulant Matrix

作　　者：程涛[1,2] 朱国宾[1] 刘玉安[1] 

机构地区：[1]武汉大学测绘遥感信息工程国家重点实验室,湖北武汉430079 [2]广西工学院汽车工程系,广西柳州545006

出　　处：《光学学报》2013年第2期165-170,共6页Acta Optica Sinica

基　　金：国家自然科学基金(40871201)资助课题

摘　　要：当前压缩感知中测量矩阵的优化是测量阶段和重构阶段采用同一矩阵的事前优化。采用了以行变换为主的测量矩阵优化算法和过渡矩阵将压缩感知的测量矩阵和重构矩阵相分离,在测量阶段采用单像素相机的0-1稀疏矩阵,在重构阶段采用近似矩阵,这是区别于传统思路的测量数据和测量矩阵的事后优化方法。理论分析和实验结果表明,优化矩阵的性能好于稀疏循环矩阵,近似矩阵和优化矩阵具有相近的性能。研究成果降低了测量矩阵工程设计和实现的难度。Current optimization of measurement matrix of compressive sensing is optimization beforehand by using the same matrix in measurement and reconstruction stages. Transition matrix and optimization algorithm mainly based on row transformation are proposed to separate the measurement matrix and reconstruction matrix of compressive sensing. 0-1 sparse matrix of single-pixel camera is adopted during measurement, while approximate matrix is adopted during reconstruction. It is a kind of afterwards optimization method of measurement data and measurement matrix, different from traditional thinking. Theory analysis and experiment results demonstrate that the characteristics of optimal matrix are better than circulant sparse matrix, and approximate matrix and optimal matrix have similar characteristics. The research results reduce the difficulty of engineering design and implementation of measurement matrix.

关 键 词：压缩感知 测量矩阵 重构矩阵 过渡矩阵 相关性 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]