Well-Posed Inhomogeneous Nonlinear Diffusion Scheme for Digital Image Denoising

We study an inhomogeneous partial differential equation which includes a separate edge detection part to control smoothing in and around possible discontinuities, under the framework ofanisotropic diffusion. By incorporating edges found at multiple scalesvia an adaptive edge detector-based indicator function, the proposedscheme removes noise while respecting salient boundaries. We createa smooth transition region around probable edges found and reducethe diffusion rate near it by a gradient-based diffusion coefficient. Incontrast to the previous anisotropic diffusion schemes, we prove thewell-posedness of our scheme in the space of bounded variation. Theproposed scheme is general in the sense that it can be used with anyof the existing diffusion equations. Numerical simulations on noisyimages show the advantages of our scheme when compared to otherrelated schemes