灰度图像复原的一种空间适应性向前向后扩散模型

摘要/Abstract

摘要：

该文考虑退化灰度图像复原问题. 首先, 作者利用时滞正则化方法定义退化图像去噪过程和去模糊过程之间的权重函数,
将激波过滤器边缘增强模型与水平集运动去噪模型相结合, 建立一种新的图像磨光增强偏微分方程. 然后, 证明该偏微分方程初值问题黏性弱解的存在唯一性. 最后, 给出该模型的部分数值算例.

关键词: 图像复原, 抛物双曲模型, 激波过滤器, 周期黏性解, 时滞正则化, 水平集

Abstract:

In this paper, a spacially adaptive smoothing and enhancing partial differential equation for image restoation,
is presented, which is coupled with time-delay regularization. In order to reverse the process of image degradation, a newly defined shock filter for edge enhancement is incorporated with a level set motion based equation for noise removal. The balance between the two processes is achieved by an edge discrimination function, which is coupled with time-delay regularization, for distinguishing boundary areas and homogeneous regions in given images. The proposed model is well-posed in terms of viscosity solutions: the existence and
uniqueness of periodic viscosity solution to the initial value problem of the equation is established. Numerical examples of some kinds of images are presented for illuminaating the efficiency of the proposed model.

Key words: Image smoothing and sharpening, Parabolic-hyperbolic equation, Shock filter, Periodic viscosity solution, Time-delay regularization, Level set motion

中图分类号:

35M10

孔令海, 郇中丹. 灰度图像复原的一种空间适应性向前向后扩散模型[J]. 数学物理学报, 2009, 29(6): 1771-1784.

KONG Ling-Hai, HUAN Zhong-Dan. A Forward and Backward Diffusion Model for Gray Level Image Restoration[J]. Acta mathematica scientia,Series A, 2009, 29(6): 1771-1784.

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