Image denoising solutions using heat diffusion equation

Abstract

The idea of this paper is to model image denoising using an approach based on partial differential equations (PDE), which describes two dimensional heat diffusion. The two dimensional image function is taken to be the harmonic, when it can be obtained as the solution to the equation describing the the heat diffusion. To achieve this, image denoising is formulated as an optimization problem, in which a function with two terms is to be minimized. The first term is called the regularization term, which is some form of energy of the image (like Sobolev energy) and the second term is called the data fidelity term, which measures the similarity between the original image and the processed image. The two terms are combined using a control parameter whose value decides which term has to be minimized more. Image denoising problem could then be solved by a simple iterative equation, derived based on the Gradient Descent method.