基于优化内积模型的压缩感知快速重构算法

A Fast Compressed Sensing Reconstruction Algorithm Based on Inner Product Optimization

针对压缩感知理论中现有重构算法耗时过长的问题,提出一种基于优化内积模型的快速重构算法,且理论推导了迭代停止条件.该算法在重构的每次迭代过程中,仅在第1次迭代时采用传感矩阵与余量的矩阵求内积运算,在后续的迭代中则通过向量运算代替矩阵求内积的运算,迭代停止时只需进行一次最小二乘法即可获得重构信号.仿真结果表明,提出的快速重构算法在保证重构信号性能的基础上,大大减少了重构时间.

The existing reconstruction algorithms in compressed sensing （CS） theory commonly cost too much time. A novel reconstruction algorithm based on inner product optimization is proposed to reduce reconstruction time. And also stopping criterion is derived from theory. The proposed algorithm computes the inner product of measurement matrix and the residual only in the first iteration during the reconstruc- tion process. In the remaining iterations, the inner product of vectors instead of matrices is calculated. Then least square calculation is done only once to reconstruct the signal after iterations stopped. Experi- ments show that the proposed algorithm reduces the reconstruction time largely without degrading the quality of the signal.