总变分图像复原方程的离散化方法

邹谋炎; 刘小军

总变分图像复原方程的离散化方法

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出版历程
- 收稿日期: 2000-01-21
- 修回日期: 2000-09-14
- 刊出日期: 2001-09-19

A DISCRETIZATION METHOD FOR TOTAL VARIATION BASED IMAGE RESTORATION EQUATION

摘要

摘要: 基于总变分的图像重建和复原导致一类最小化问题,它归结为解一个非线性椭圆型偏微分方程。为了得到数值解,必须将问题线性化和离散化。C.R.Vogel和M.E.Oman等人(1996)的定点迭代是一个良好的线性化方法。然而文献中已报道的离散化方法需要微分方程数值解的工具,比较繁杂。该文提出一种新的离散化方法,它只需要图像处理中的常规技术。图像反降晰和噪声抑制的实验结果表明该文的结果不亚于文献中报道的结果。
- 恢复; 重建; 总变分; 定点迭代
Abstract: Total variation based image restoration and reconstruction lead to a kind of minimization problem that turns out to be a nonlinear integro-differential equation of elliptic type. An effective linearization and. discretization method is essential for solving the problem. The fixed point iteration proposed by C. R. Vogel and M. E. Oman(1996) is an elegant scheme of linearization. For discretization of the problem, however, the reported methods mostly involve the skills in numerical solutions of differential equations that are not amiable for the image processing community. In this paper, a discretization method is presented that needs only con- ventional technique for image processing. The method can simplify the implementation of the fixed point iteration scheme. The experimental results of image restoration and image denoising are used to justify the method.

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