随机投影阵下的界约束总变分图像恢复算法

主要研究以交替方向法为基础的总变分图像恢复模型,结合约束优化问题以及快速迭代技术,提出了一种约束总变分图像恢复的快速算法。对总变分模型添加范围约束,利用交替方向法进行求解,把原问题转化为3个子问题,分别用迭代阈值法、快速傅里叶变换法以及投影法进行求解。把快速迭代技术应用于迭代阈值法来提高计算效率,利用非精确计算法来克服系数矩阵为随机投影阵带来的傅里叶变换的计算费时问题。数值试验结果〖JP2〗表明,针对随机投影阵下的约束总变分问题,新方法在提高计算效率的同时还能得到很好的图像恢复效果。

Algorithm for bound constrained total variation image restoration from random projections

Based on the alternating direction method （ADM）, the total variation image restoration model is mainly researched. A fast algorithm for constraining the total variation image restoration is proposed combined with the constrained optimization problem and the fast iterative technique. The primal problem is transformed into three sub-problems, and the iterative threshold method, Fourier transform method and projection method are used to solve the sub problems respectively. The fast iterative technique is applied to the iterative threshold method to accelerate the efficiency of the algorithm. The inexact method can be used to overcome the slow computation speed of the Fourier transform for the random projection matrix. For total variation image restoration from random projection numerical results demonstrate that the proposed algorithm can improve the computation efficiency and image recovery effect.