A perceptual phenomena that has received considerable attention in the medical imaging community is the influence of image variability on signal-detection tasks. This subject is relevant to medical imaging because detection tasks are a common use of diagnostic images, and these images have two well known sources of variability [1-10]. The first source of variability results from system noise obtained during image acquisition. System noise is usually defined by the physical processes that govern the imaging device such as counting statistics, film-grain noise, or amplifier noise. The other source of variability in medical images has to do with the variable nature of the objects being imaged. Patient-to-patient variability - sometimes referred to as "anatomical" noise - is more difficult to characterize than system noise but can be an important factor that limits detection performance.
For detection tasks in the presence of image variability, a general approach to modeling human observers has been to use signal detection theory to define mathematical algorithms that perform the same detection task as the human observer. These sorts of models are often referred to as "model observers" because they mimic the role (as well as, it is hoped, the performance) of a human observer. Linear observers are an important class of model observers because they have been widely studied for simple detection tasks in noise, where there is no signal uncertainty  (see Chapter 9).
In medical imaging, predictive models of task performance have an important application as an aid to optimizing diagnostic-imaging systems. The basic precept of objective assessment of image quality is that the best system will result in images that allow an observer (usually a clinician) to best perform a diagnostic task of interest . In principle then, the process of optimizing imaging systems involves numerous evaluations of human-observer performance in the task of interest. However, human-observer studies are costly and time consuming. Predictive models for detection performance would greatly reduce the need for these studies and allow for tuning more parameters in the diagnostic-imaging chain .
This chapter considers the most basic detection task, signal-known-exactly (SKE) detection. The SKE task epitomizes the notion of controlled stimuli. The signal-present images of an SKE task have a fixed (nonrandom) signal profile that is fixed at a given location, orientation, and size. In principle, the signal contrast is also presumed to be fixed, although some experimental methodologies adjust the signal contrast to achieve a predetermined level of performance . SKE tasks are certainly simpler than clinical detection tasks which contain varying degrees of uncertainty in the signal parameters. However, this simplicity can be an advantage in basic studies of perceptual performance because it removes possible confounds from the resulting observed data. For example, consider the detection of a signal at an unknown location in an image and in the presence of image noise. This is not an SKE detection task because of uncertainty in the signal location. Poor performance in this task by human observers could be explained by some combination of image-noise effects and an inefficient visual search strategy.
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