Preface; Contents; List of Figures; List of Tables; 1. Introduction; 2. A collection of linear inverse problems; 3. The basics about linear inverse problems; 4. Regularization in Hilbert spaces: Deterministic and stochastic approaches; 5. Maxentropic approach to linear inverse problems; 6. Finite dimensional problems; 7. Some simple numerical examples and moment problems; 8. Some infinite dimensional problems; 9. Tomography, reconstruction from marginals and transportation problems; 10. Numerical inversion of Laplace transforms; 11. Maxentropic characterization of probability distributions
Summary
This book describes a useful tool for solving linear inverse problems subject to convex constraints. The method of maximum entropy in the mean automatically takes care of the constraints. It consists of a technique for transforming a large dimensional inverse problem into a small dimensional non-linear variational problem. A variety of mathematical aspects of the maximum entropy method are explored as well