INFORMATION-THEORETIC IMAGE-FORMATION

The emergent role of information theory in image formation is surveyed . Unlike the subject of information-theoretic communication theory, in formation-theoretic imaging is far from a mature subject, The possible role of information theory in problems of image formation is to provi de a rigorous framework for defining the imaging problem, for defining measures of optimality used to form estimates of images, for addressi ng issues associated with the development of algorithms based on these optimality criteria, and for quantifying the quality of the approxima tions. The definition of the imaging problem consists of an appropriat e model for the data and an appropriate model for the reproduction spa ce, which is the space within which image estimates take values. Each problem statement has an associated optimality criterion that measures the overall quality of an estimate. The optimality criteria include m aximizing the Likelihood function and minimizing mean squared error fo r stochastic problems, and minimizing squared error and discrimination for deterministic problems. The development of algorithms is closely tied to the definition of the imaging problem and the associated optim ality criterion. Algorithms with a strong information-theoretic motiva tion are obtained by the method of expectation maximization, Related a lternating minimization algorithms are discussed. In quantifying the q uality of approximations, global and local measures are discussed, Glo bal measures include the (mean) squared error and discrimination betwe en an estimate and the truth, and probability of error for recognition or hypothesis testing problems. Local measures include Fisher informa tion.