A central problem in Image Processing is as follows: Given a 'grainy'/ 'noisy' image, eliminate as much of the noise and preserve as much of the original image as possible, while minimizing computational memory and time. In this project I investigate a method of doing this: relaxed inverse -- scale -- space flow. I implement two algorithms based on this method: linear and ROF. I then consider a possible improvement on these two algorithms called bilateral filtering. I use a computer implementation of these algorithms on two test images (a top view of an army tank in a desert , and a photograph of a woman -- 'Elaine'). I comment on the strengths and weaknesses of each algorithm. Possible criteria for a 'best' algorithm: (1) How much noise is eliminated, (2) how much of the original image is preserved, (3) How much computer memory is used for each algorithm, (4) how fast can each image be 'denoised'.