A unified approach for hierarchical imaging based on joint hypothesis testing and parameter estimation

The authors present a single formulation for constrained imaging that fuses the problem of joint estimation of the continuous parameters using MAP (maximum a posteriori) and conditional-mean estimators with that of performing generalized Bayes hypothesis testing for the symbolic imaging variables. Coupling this with recent results on representing regular grammars via Gibbs´ distributions makes it possible to incorporate into a single hierarchical framework the stochastic constraints relevant to continuous-valued parameters as well as language-theoretic constraints on the symbolic variables. The authors also present a method for performing the required computations on a massively parallel architecture, which makes it possible to update every variable at every level in the hierarchy in parallel. The conclusions obtained are supported with results for a Poisson imaging problem computed on a DAP-500 massively parallel processor with 1024 processing elements