Efficiency of the Human Observer in LROC Studies

In medical imaging, a important task is the detection of a lesion or defect in a noisy background. For signal-known-exactly (SKE) detection tasks, a figure of merit (FOM), the area under the receiver operating characteristic (ROC) curve (AROC), can be used to evaluate the task performances and to compare the data processing methods. The objective of the SKE task is to determine whether the image contains the lesion or not. However, a more clinically revevant task requires the observer to search for the location of the lesion. This is one form of a signal-known-statistically (SKS) task, with location known only statistically. We now focus on the mathematical description of the detection task with location uncertainty. A test image g is either lesion-absent or with a lesion present at one of J locations, and the objective of an observer is to determine which class the test image g belongs to. This task is similar to a (J +1)-class classification problem (also known as multiple hypothesis-testing problem) with classes (hypotheses) expressed as: where H is a imaging operator that maps an N × 1 vector of object (either signal-absent or signal-present) to an M × 1 vector of image data g and n is an M × 1 vector of measurement noise with mean zero. For class H 0 , the test image g consists of background image data Hb plus zero-mean noise, but has no signal. For class H j , g also contains signal image data Hs j with signal (lesion) s j present at the j th location. We assume that an observer performs this task by computing a scalar test statistic t based on g. For a 2-class SKE detection problem, this scalar test statistic is compared to a threshold τ to decide signal-present if t(g) > τ and signal absent if t(g) < τ. For each threshold τ , we can calculate the probability of true positive P T P (τ) indicating the probability of deciding signal-present when a signal is actually present , and the probability of false positive P F P (τ) indicating the probability of deciding signal-present when a signal is not actually present. An ROC curve can be generated by ploting P T P (τ) as a function of P F P (τ) as sweeping the threshold τ. Fig. 1 shows a hypothetical ROC curve. The area under the ROC curve, AROC, is …