An Image Restoration Algorithm In The Matrix Form

Nowadays our society has entered the era of the digital information, image is one of the essential parts. In the process of generation and transmission, image becomes fuzzy because some noise pollution. Therefore it has a great influence on the postprocessing. Image denoising is an important part in the image processing which directly affects the results of subsequent processing and analysis. The PDE-based method is one of the most significant techniques in image processing. Its numerical methods have important theoretical and practical significance. In this paper, we consider some existing partial differential equation models for image denoising. We also make numerical analysis for these models and use different discrete schemes and different boundary conditions to have experiments.We present some innovative results as follows:Firstly, the Crank-Nicholson semi-implicit difference scheme is applied to discrete the Rudin-Osher-Fatemi model which was proposed by Rudin et al. in1992. The semi-implicit discrete scheme avoids the shortcomings of instability and many iterative numbers that the explicit discrete scheme needs.Secondly, we propose a semi-implicit image denoising algorithm in the matrix form. Here we adopt three denoising models-ROF、(BV,L1) and NROF model to have numerical experiments. We also adopt Dirichlet boundary conditions, periodic boundary conditions, Neumann boundary conditions, anti-reflecting boundary conditions and mean boundary conditions to have numerical experiments.At last, we adopt the explicit discrete scheme and the Crank-Nicholson semi-implicit algorithm in the matrix form to have the experiments. The results show that the Crank-Nicholson semi-implicit scheme is more efficient than the explicit discrete scheme. The NROF model can get better restored results than the ROF model. The anti-reflecting boundary conditions and mean boundary conditions can keep the boundary better than the others.