Channelized hotelling observer performance for penalized-likelihood image reconstruction

What type of regularization method is optimal for penalized-likelihood image reconstruction when the imaging task is signal detection based on a channelized Hotelling (CHO) observer? To answer such questions, one would like to have a simple analytical expression (even if approximate) for the performance (SNR) of the CHO observer given different reconstruction methods. Bonetto, Qi, and Leahy (IEEE T-NS, Aug. 2000) derived and validated one such expression for penalized-likelihood (aka MAP) reconstruction and the Signal Known Exactly (SKE) problem using linearizations and local shift-invariance approximations. This paper describes a further simplification of the analytical SNR expression for the more general case of a Gaussian-distributed signal. This simplification, based on frequency-domain decompositions, greatly reduces computation time and thus can facilitate analytical comparisons between reconstruction methods in the context of detection tasks. It also leads to the very interesting result that regularization is not essential in this context for a large family of linear observers.