稀疏图像重构非凸Lp问题的分裂方法

摘要/Abstract

摘要：

由于稀疏图像重构Lp(0<p<1)问题是一个非凸问题。利用半二次罚函数方法将非凸Lp问题分裂成X子最优化问题和Y子最优化问题。对于X子问题,通过光滑函数求导的方法给出其闭形式解。对于Y子问题,通过阈值收缩不动点迭代公式进行求解。对这两个子问题的交替求解过程建立了压缩感知中的稀疏图像精确重构Lp问题的分裂算法。通过MR图像进行数值模拟,实验结果表明,与L1问题求解的分裂算法相比,非凸Lp问题的分裂方法具有更高的计算精度和更低的抽样率。

关键词: 压缩感知, 非凸优化, 稀疏图像, 图像重构

Abstract:

Lp(0<p<1) problem in sparse image reconstruction is a non-convex optimization problem.The non-convex Lp problem has been splitted into two sub-problems:X sub-problem and Y sub-problem by a half-quadratic penalty method.The closed form solution for X sub-problem could be obtained by the derivative of smooth function.And the solution of Y sub-problem was solved via shrinkage fixed point iterative formula.The splitting algorithm to solve Lp problem for sparse image reconstruction in compressive sensing was estabished by the alternating minimization method for the two sub-problems.Some different kinds of MR images was employed to test in the numerical experiment,and the results demonstrate that the non-convex splitting method is not only more accuracy but also lower sampling rate than convex splitting method in the sparse image reconstruction.

Key words: compressive sensing, non-convex optimization, sparse image, image reconstruction

中图分类号:

TP391

朱永贵, 刘平, 丛佳. 稀疏图像重构非凸Lp问题的分裂方法[J]. 吉林大学学报(工学版), 2013, 43(增刊1): 55-59.

ZHU Yong-gui, LIU Ping, CONG Jia. Splitting method to solve Lp problem in sparse image reconstruction[J]. 吉林大学学报(工学版), 2013, 43(增刊1): 55-59.

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