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.

- [1] H. H. Bauschke and J.M. Borwein, "On projection algorithms for solving convex feasibility problem," SIAM Review, submitted.
- [2] J.M. Borwein and A. S. Lewis, "Duality relationships for entropy-like minimization problems," SIAM J. Control and Optim., 29(1991), 325-338.
- [3] J.M. Borwein, R. K. Goodrich, and M. A. Limber, "A comparison of entropies in the underdetermined moment problem," Numerical Functional Analysis and Optimization, submitted.
- [4] M. A. Limber, T. A. Manteuffel, S. F. McCormick and D. S. Sholl, "Optimal Resolution in Maximum Entropy Image Reconstruction from Projections with Multigrid Acceleration," Proceedings of the Sixth Annual Copper Mountain Conference on Multigrid Methods, Eds. S. F. McCormick and T. A. Manteuffel, 1993