The MomEnt+ project is a computational engine intended to implement and expand the applicability of much of the maximum entropy theory that has been developed in the past few years. The project is not a single package or piece of code, but rather a diverse combination of computer programs, theory, and contacts, designed to enhance the participants' collective knowledge of numerical optimization, real world issues, and optimization theory, as well as to offer our mathematical and computational skills to a variety of nonmathematical researchers.
The immediate goal is to design and implement a collection of computer algorithms and codes, and to make contacts in image processing, geophysics, electrical engineering, statistics and wherever else we might find interest in our activities.
We have developed a TOOL that allows one to reconstruct any given number of moments of a user supplied input function. There are a number of types of entropy to chose from. Uniform or Gaussian noise can be added to the recontruction problem and Newton, Conjugate Gradient or Barzilai-Borwein numerical methods can be selected for the computations.
Persons and research groups who believe that the work of the MomEnt+ project may be of interest to them are urged to contact Ron Haynes of the CECM.
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.
Other interesting entropy/optimization related links are:
/ SFU / CECM / ~moment /