Linear estimation theory applied to the evaluation of a priori information and system optimization in coded-aperture...

Linear estimation theory is developed in the context of object reconstruction from data obtained by a general shift-variant imaging system. The formalism adopts nonstationary first- and second-order statistics of the object and noise classes as priori information. In addition, a metric for system optimization that depends on the a priori information is presented. The role of this a priori information as derived from several different training sets is then studied with respect to reconstruction performance for various noise levels in the data, using a tomographic coded-aperture system as the model. In a separate experiment, a simple coded-aperture system is optimized to a particular object class, and the results are compared with those from an earlier optimization experiment.