Research On Some Difference Numerical Methods Of Image Denoising Based On Fractional PDE

Image denoising numerical methods based on Space Fractional Partial Differential Equations is an important direction of image denoising field, and its study of numerical methods has important theoretical significance and practical value.This paper constructs implicit difference scheme and θ-difference scheme for solving the Space Fractional image denoising model (TV model). And the existence and uniqueness of solutions, the stability and convergence of these schemes are analyzed. We also make research on how to construct fractional differential operator mask and to make these differential operator masks better.For the Space Fractional TV model, the implicit difference scheme is analyzed to be unconditional stable, convergent, existence and uniqueness of solution. The 9-difference scheme is analyzed to be conditional stable, convergent, existence and uniqueness of solution.According to the theoretical analysis and the numerical experiment, the implicit difference scheme and the θ-difference scheme are effective to solve the Space Fractional TV model. Under appropriate conditions, the denoising results of the θ-difference scheme are better than the implicit difference scheme, and these two methods are both better than fractional differential operator mask method. The improved fractional differential operator mask method of this paper is effective to solve the Space Fractional TV model. The denoising results of the improved fractional differential operator mask method are better than the existing fractional differential operator mask method, but worse than the implicit difference scheme and the θ-difference scheme.Theoretical analysis and numerical experiments demonstrate the implicit difference scheme, the θ-difference scheme and the improved fractional differential operator mask method are effective to solve Space Fractional TV model.