一种面向二维观测模型的压缩感知重构算法

A 2-Dimensional Measurement Model-Oriented Compressed Sensing Reconfiguration Algorithm

针对目前二维信号压缩感知重构时,常采用的一维化手段效率低、重构性能有待提高等缺陷,基于二维观测模型,提出一种新的压缩感知重构方法,并证明了其有效性。算法通过两个独立感知矩阵对二维信号的行列同时进行压缩感知,并考察信号的整体重构,缓解了传统算法引入的重构人为效应以及问题规模扩张带来的重构压力。理论分析和实验表明,新算法成功重构概率、重构信噪比等性能优于现有典型二维信号重构方法,且其运算复杂度较之一维化方法有所降低。

The existing reconstruction algorithms for 2-D signals, most of which convert the original signals into I-D signals, could be more efficient and accurate. Based on the 2-Dimensional measurement model （2-DMM）, a novel recovery algorithm is proposed and then its effectiveness is proved. In 2-DMM, the rows and columns of 2-D signals are measured simultaneously by two independent sensing matrixes. The new algorithm reconstructs the signals as a whole. It relieves the artificial effects and scale expansion caused by the traditional algorithms. Both theoretical analysis and experiment simulation demonstrate that the recovery probability and Reconstruction-SNR performance of the new algorithm are better than those of the existing reconfiguration algorithms under the condition of 2-D measurement. While the operation complexity of the new algorithm is lower than the counterpart of 1-D conversion algorithms.