【摘要】 通过介绍传统非线性扩散方程在图像处理中的一般应用,引入了一类含间断系数的非线性扩散模型,并利用非线性系数正则化处理的方法及粘性解该类模型中的研究结果,得到了该模型的适定性理论.给出的一些具体数值实验结果表明,该非线性扩散模型是图像修复问题的一种比较理想的方法.更多还原

【Abstract】 One class of nonlinear diffusion equation in dealing with digital image inpainting was introduced. A general method in dealing with the well-posedness of the initial-boundary value problem for this kind of nonlinear equations was discussed. Some numerical experiment results in image inpainting were given, which show that the nonlinear diffusion model introduced in this paper is suitable in image inpainting. This paper proposed one method in image inpainting with both of theoretical and practical value.更多还原