Besov空间下迭代全变差正则化的图像恢复模型

摘要

在Besov空间下,提出了一种用于图像恢复领域的迭代全变差正则化模型.通过使用一个加权的参数序列,给出了一个迭代正则化的变分问题,这个变分问题实际上是一个小波软硬阈值结合的迭代程序.给出了新模型的停止标准和一些好的性质,如单调性和收敛性等.数值实验表明与传统去噪方法相比,新方法不仅能较好地恢复图像,而且收敛速度较快.%An iterative regularization procedure in Besov spaces for image restoration is generalized. By using a suitable sequence of penalty parameters,the issue of solvability of minimization problems arising in each step of the iterative procedure is solved. The generalized iterative regularization procedure can be considered as a combination of soft-thresholding and hard-thresholding. Moreover, an effective stopping criteria and convergence result for the procedure are obtained. The numerical results indicate that the iteration procedure yields high-quality reconstructions and converges faster than the Xu-Osher method.