中文摘要：

理论证明了可压缩信号各列及其对应稀疏变换域系数矩阵各列具有相同的能量和方向信息;测量数据各列的能量和方向信息本质上反映了可压缩信号各列的能量和方向信息;图像稀疏变换域系数矩阵相邻列具有极高的相似性。基于二维压缩感知模型在传统的OMP算法中引入信号方向信息,构建了2DDOMP算法,取得了更好的图像重构效果,避免了当前压缩感知重构算法单纯依靠测量数据的盲目性和不确定性。基于信号方向信息的重构算法设计思想可用于改造优化各类重构算法,是对当前压缩感知研究的重要补充。

英文摘要：

It＇s proved by theory analysis that each column of compressible signals has same energy and direction information with each corresponding column of coefficient matrix in sparse transform domain.The energy and direction information of each column of the measurement data reflect the energy and direction information of each column of compressible signals in nature.The adjacent columns of image coefficient matrix in sparse transform domain are with high similarity.Based on two-dimensional compressive sensing model,signal direction information is introduced into the traditional OMP algorithm and two-dimensional direction orthogonal matching pursuit（2DDOMP）algorithm is constructed.Better image reconstruction results are achieved.The blindness and uncertainty of current compressed sensing reconstruction algorithm relying solely on measurement data are avoided.The design idea of reconstruction algorithm based on signal direction information can be used to reform and optimize various reconstruction algorithms.