Figures of merit for optimizing imaging systems on joint estimation/detection tasks

Previously published work on joint estimation/detection tasks has focused on the area under the Estimation Receiver Operating Characteristic (EROC) curve as a figure of merit for these tasks in imaging. A brief discussion of this concept and the corresponding ideal observer is included here, but the main focus is on three new approaches for system optimization on these joint tasks. One of these approaches is a generalization of Shannon Task Specific Information (TSI) to this setting. The form of this TSI is used to show that a system optimized for the joint task will not in general be optimized for the detection task alone. Another figure of merit for these joint tasks is the Bayesian Risk, where a cost is assigned to all detection outcomes and to the estimation errors, and then averaged over all sources of randomness in the object ensemble and the imaging system. The ideal observer in this setting, which minimizes the risk, is shown to be the same as the ideal EROC observer, which maximizes the area under the EROC curve. It is also shown that scaling the estimation cost function upwards, i.e making the estimation task more important, degrades the performance of this ideal observer on the detection component of the joint task. Finally we generalize these concepts to the idea of Estimation/Detection Information Tradeoff (EDIT) curves which can be used to quantify the tradeof between estimation performance and detection performance in system design.