基于2D-DCT等效矩阵的压缩成像  

Compressive imaging using 2D-DCT equivalent matrix

作　　者：刘巍 赵春晖[1] 

机构地区：[1]哈尔滨工程大学,哈尔滨150001

出　　处：《仪器仪表学报》2010年第7期1576-1582,共7页Chinese Journal of Scientific Instrument

基　　金：国家自然科学基金(批准号:60672034)资助项目

摘　　要：压缩感知理论允许人们通过少于采样定理要求的测量值重建信号。受到测量矩阵设计方面的限制,使用快速的贪婪算法重建时需要一个稀疏分解矩阵。目前通常根据一维变换构造稀疏分解矩阵,无法体现图像的结构信息。本文通过构造二维离散余弦变换(2D-DCT)等效矩阵来解决这一问题,通过重建图像二维变换系数的手段达到保护结构信息的目的。该等效矩阵与图像列序向量相乘得到的系数均来自图像2D-DCT变换,所以使用这种等效矩阵作为稀疏分解矩阵可以令贪婪算法重建的结果与图像2D-DCT变换系数相同,进而令基于2D-DCT等效矩阵的压缩成像可以在使用快速贪婪算法的同时保持图像的二维结构信息,并且不增加软硬件成本,实验显示该方法有效改善了图像重建的效果。Compressive sensing theory allows people to reconstruct signal from less measurements than those sampling theorem requires. Restricted by measurement matrix design, a sparse decomposition matrix is required when using fast greedy algorithm. At present, sparse decomposition matrix is constructed according to one-dimensional transform and the structural information of the image can not be reflected. In this paper, we construct a 2D-DCT equivalent matrix to solve the problem and achieve the purpose of protecting the structural information through reconstructing two-dimensional transform coefficients. The image sequence vector and equivalent matrix are multiplied to produce the same coefficients as those of 2D-DCT transform of the image. Using 2D-DCT equivalent matrix as sparse decom- position matrix can make compressive imaging maintain the two-dimensional structural information of the image while using fast greedy algorithm, which does not increase hardware and software costs. Experiment results show that the proposed method can improve the image reconstruction results.

关 键 词：压缩感知 压缩成像 稀疏分解 2D—DCT等效矩阵 图像重建 

分 类 号：TN911.73[电子电信—通信与信息系统]