Closeness of 2 Images in High Dimensional Space

Goal: One method that is often used to denoise images is the direct method of calculus of variations. In this method, the assumption is that the perfectly denoised image is a function that minimizes the value of a particular functional, for example, total variation. Given a starting image (function) with noise, one makes a small change to the image (function) that decreases the value of the functional as much as possible. Under nice conditions, this iterative adjustment of the image eventually converges. If the original image is available, one can measure the success of the method by checking how closely the denoised image approximates the original. The project explores what happens to the intermediate and final images under this process if various functionals are used. Alternatively, a student could explore different ways of measuring the closeness of two images.