改进的压缩感知量测矩阵优化方法

Improved optimization algorithm for measurement matrix in compressed sensing

压缩感知理论中信号的重建要求量测矩阵与稀疏变换基之间的互相关性要尽可能小。以降低二者互相关性为目的,研究了一种改进的基于变步长梯度下降的量测矩阵优化方法。该方法利用梯度下降法更新步长,并基于模拟退火中的降温思想引入学习速率因子来进一步调节步长的变化,提高算法的收敛速度,改善算法的性能。仿真结果表明,使用变步长梯度下降法优化后的量测矩阵与稀疏变换基的互相关系数在零附近的分布更加集中,量测矩阵的优化速度快并且重构图像的峰值信噪比提高。因此,所提方法优化所得的量测矩阵无论是降低互相关性还是提高图像重建质量都具有良好的性能。

The signal recovery performance of compressed sensing （CS） requires that the cross correlations between the measurement matrix and sparse transformed matrix should be as small as possible. In order to re- duce the cross correlations, an varied step gradient descent algorithm is studied and si-mulated annealing （SA） learning rate factor is introduced to adjust the step function. The simulation results demonstrate that due to the adaptive adjustment of step length in the iteration process, the speed of optimizing matrix is fast, more mutual coherence coefficients are distributed around zero, and the peak signal to noise ratio of reconstructed image is improved with the optimized measurement matrix. The improved algorithm has good performance in achieving lower mutual coherence and improving reconstruction performance.