Stochastic approaches to inversion problems in optics

Image restoration, image smoothing, and probability law estimation are important inverse problems in optics. Within the past 10 or so years, much progress has been made toward their resolution. These problems are often ill-posed mathematically. However, such concepts as maximum entropy, maximum likelihood, binay decision discrimination, median window filtering, MAP estimation, and minimum Fisher information have proven invaluable in regularising, or reducing, the ill-posed nature of the problems. In particular, those concepts which measure uncertainty or disorder have played a central role. Given noise-prone data, concepts that describe maximal disorder (maximum entropy, minimum Fisher information, minimal bina y discrimination) exert a smoothing influence on the solutions that drastically reduces noise propagation into the output. Given insufficient but noise-free data, as in the probability estimation problem, the principle of minimum Fisher information, in particular, creates smooth estimates which, oftentimes, are physically correct as well.