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.