Function Reconstruction, the MomEnt+ Project

Headed by Mark A. Limber, the MomEnt+ project is the computational engine behind the convex entropy optimization research at the CECM. The name "MomEnt+" is derived from "Moment problems solved via Entropy maximization with Positivity". However, we are not exclusively working on moment problems, except in a general sense, nor are we restricting ourselves to maximum entropy methods.

The underlying problem we study is Ax = b where A : X -> R^n is a continuous linear operator and X is some function space. Since this is generally an underdetermined problem, we can pick a solution via an optimization criterion, for example, the solution to

inf { f(x) : Ax = b, x >= 0 }

where f:X -> R is a suitable convex functional. We have implemented the theory of convex duality as developed in [2] in both a Maple and C environment [3] to solve such problems. We are also concentrating on other computation methods, including projection [1] and multigrid [4] methods.

We have made contacts with the medical imaging groups at Vancouver General Hospital and TRIUMF, the government research centre located in Vancouver. These and other contacts will keep this project application oriented and force us to address real world issues that arise in applications, in particular, extremely noisy data.