Research On Several New Numerical Methods Of Two Models In Image Denoising

The study on the numerical methods of Partial Differential Equations (PDEs) for image denoising which play an important role in the field of image processing has important theoretical significance and practical value. This paper researches the several new numerical solutions of two typical PDE models (the mean curvature motion (MCM) equation and the regularized P-M (CLMC) equation) for image denoising. The compact alternating direction implicit (compact ADI) method is established for MCM equation. For CLMC model, the improved Additional Operator Splitting (AOS) algorithm has been used to construct AOS-CN method, AOS-explicit-implicit method and AOS-implicit-explicit method, AOS-three time layer implicit method and AOS-compact method. The stability, convergence and accuracy of the methods are analyzed.The theoretical analysis and numerical experiments show that the compact ADI method is a high precision and unconditionally stable difference method. The four unconditionally stable difference methods for CLMC model increase the time accuracy of traditional AOS method from one order to second order. With the same iterations, the methods constructed in this paper can preserve the edge and detailed information better, while denoising the noisy image. Their comprehensive performance are better than the AOS method. The numerical methods constructed in this paper are effective in image denoising, especially the AOS-three time layer implicit method of CLMC model for image denoising has practical application value.