一种基于矩阵格式的半隐式图像去噪算法

A Semi-implicit Image Denoising Algorithm in Matrix Form

图像去噪是进一步处理图像的必要步骤和关键环节之一.首先针对Rudin等在1992年提出的ROF模型,利用Crank-Nicolson半隐式差分格式进行离散,克服了显式离散格式的不稳定性和迭代次数多的缺点;其次在求解过程中提出了一种基于矩阵格式的半隐式新算法,并将新算法应用于三种边界条件——零边界条件、周期边界条件和Neumann边界条件进行数值试验;数值试验结果表明采用Crank-Nicolson半隐式离散格式去噪的效果优于显式离散格式;同时,Neumann边界条件能很好的保持图像边界的连续性.

The image denoising is one of the essential steps and key links in the process of image pro-cessing. Firstly, the Crank-Nicolson semi-implicit difference scheme is applied to discrete the famous Ru- din-Osher-Fatemi model which was proposed by Rudin et al. in 1992, overcoming the shortcomings of in- stability and many iterative numbers that the explicit discrete scheme has. Secondly, a semi-implicit image denoising algorithm in the matrix form is proposed. In the numerical experiment, we adopt Dirichlet boundary conditions, Periodic boundary conditions and Neumann boundary conditions. The experimental results show that the Crank-Nicolson semi-implicit scheme in matrix form is efficient and the Neumann boundary conditions keep the continuity of boundary.