Objective assessment of sonographic quality I: Task information

In this paper, we explore relationships between the performance of the ideal observer and information-based measures of class separability in the context of sonographic breast-lesion diagnosis. This investigation was motivated by a finding that, since the test statistic of the ideal observer in sonography is a quadratic function of the echo data, it is not generally normally distributed. We found for some types of boundary discrimination tasks often required for sonographic lesion diagnosis, the deviation of the test statistic from a normal distribution can be significant. Hence the usual relationships between performance and information metrics become uncertain. Using Monte Carlo studies involving five common sonographic lesion-discrimination tasks, we found in each case that the detectability index dA² from receiver operating characteristic analysis was well approximated by the Kullback-Leibler divergence $J$, a measure of clinical task information available from the recorded radio-frequency echo data. However, the lesion signal-to-noise ratio, SNRI², calculated from moments of the ideal observer test statistic, consistently underestimates dA² for high-contrast boundary discrimination tasks. Thus, in a companion paper, we established a relationship between image-quality properties of the imaging system and $J$ in order to predict ideal performance. These relationships provide a rigorous basis for sonographic instrument evaluation and design.