基于光滑l_p范数的压缩感知图像重构算法

A Image Reconstruction Algorithm of Compressed Sensing Based on Smooth l_p Norm

针对压缩感知理论中的图像重构问题,提出一种基于光滑l_p(0<p<1)范数的图像重构算法。首先,将重构问题转化为基于最小l_p范数的优化问题进行求解;其次,构造光滑函数逼近l_p范数;接着,通过离散化光滑函数的解序列来逼近最小l_p范数的最优解;最后,以Lena图像为例对算法进行了仿真研究。结果表明,相比于传统的OMP(Orthogonal Matching Pursuit)算法和IRLS(Iteratively Reweighted Least Squares)算法,该算法不仅提高了图像重构质量,而且大幅减少了重构时间。

In order to solve the problem of image reconstruction in compressed sensing theory, an image reconstructionalgorithm based on smooth lp（ 0 〈p 〈 1 ） norm is proposed. Firstly, the reconstruction problem wastransformed into solving the optimization problem based on the minimum /pnorm. Secondly, the smooth functionwas constructed to approximate /pnorm. Then, the optimal solution of the lp norm was obtained by discretizingthe sequence of the smoothing function. Finally, the Lena image was taken as an example to simulate the algorithm.The results show that compared with the traditional OMP algorithm and IRLS algorithm, the quality ofimage reconstruction is improved, and the reconstruction time is greatly reduced.