Besov空间下迭代全变差正则化的图像恢复模型

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。

Iterative total variation regularization for image restoration in Besov spaces

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.