Characterization of task performance based on maximum a posteriori reconstructions

The performance of two related tasks, object detection and object amplitude estimation, is investigated. These tasks are related because the best amplitude estimate is the appropriate decision variable for the detection task. Different results have been observed for these two tasks as a function of λ (a scalar which controls the strength of regularization) in a study restricted to images containing a mixture of high- and low-contrast nonoverlapping disks on a zero background. It has been found that in maximum a posteriori reconstructions the contrast of the low-contrast disks relative to the background decreases steadily as λ increases. Thus the estimates for the amplitude of these disks deviate from their actual values. On the other hand, the detectability index does not change as quickly. The reason for this is that detectability is based on the separation of the estimate of the amplitude of the object relative to the estimate of the background value compared to their RMS deviations. The choice of λ obviously becomes an important issue as it affects the bias in the estimated amplitude. It is postulated that the same behavior holds for many other types of Tikhonov regularization