Recovery of blocky images from noisy and blurred data

The purpose of this investigation is to understand situations under which an enhancement method succeeds in recovering an image from data which are noisy and blurred. The method in question is due to Rudin and Osher. The method selects, from a class of feasible images, one that has the least total variation. Our investigation is limited to images which have small total variation. We call such images "blocky" as they are commonly piecewise constant (or nearly so) in grey-level values. The image enhancement is applied to three types of problems, each one leading to an optimization problem. The optimization problems are analyzed in order to understand the conditions under which they can be expected to succeed in reconstructing the desired blocky images. We illustrate the main findings of our work in numerical examples.