Reconstructing Images as Piecewise Smooth Func- tions

Leclerc’s approach to image reconstruction consists of finding the shortest description of the data (an image) as a model (reconstruction) plus noise [5]. The approach poses two design problems: 1. Define an appropriate description language for image models and noise, 2. Derive an objective function and conceive an optimization algorithm that finds good local minima. Leclerc proposed to model images as piecewise low order polynomials and to describe models in terms of region boundaries (discontinuity set) and polynomial coefficients. In this report I describe Leclerc’s methodology, and, adopting his image model and description language, derive an objective function within this methodology. I discuss the differences of my result with Leclerc’s objective function, sketch the optimization algorithm and give expressions for the gradient of my objective function.