See studies by Abbey and Barrett, 5 Burgess et al., 6 and Bochud et al. A great deal of research has been done on the performance of nonoptimal observers such as human observers and model observers in different types of backgrounds. 3 Clarkson and Barrett 4 worked out the ideal-observer test statistic for a number of situations in which the statistics of the backgrounds followed certain distributions, including Gaussian and Laplacian distributions. Researchers often resort to unrealistic assumptions that dramatically simplify the math, such as assuming fixed backgrounds. Thus computing the ideal observer is often considered either too difficult or impossible for image data, which tend to be large e.g., images of size 512 × 512 are characterized by a probability density function of a 512 2 random vector.
The ideal observer requires complete knowledge of the statistics of the images or image data. Furthermore, it is often useful to compare the performance of other observers relative to the performance of the best observer. That is, the ideal observer is a useful tool for comparing and optimizing imaging systems. (For simplicity, any reference to ideal observers from now on implies Bayesian ideal observers.) Because no other observer can outperform the ideal observer by these standards, it is reasonable to use ideal-observer performance as a figure of merit in comparing imaging systems. The class of ideal observers includes the Bayesian ideal observer, 2 which sets an absolute upper limit on task performance as measured by most common figures of merit. An ideal observer is a mathematical construct that is optimal in a well-defined sense. Observers can be human, human-model, or ideal observers. 1 Tasks in medical imaging are typically detection tasks, e.g., determining whether a tumor is present, or estimation tasks, e.g., determining the value of a clinically relevant parameter. We advocate the position that to properly quantify image quality one must clearly define the task that is to be performed and the observer who will be performing this task.
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