Image quality can be defined objectively in terms of the performance of some "observer" (either a human or a mathematical model) for some task of practical interest. If the end user of the image will be a human, model observers are used to predict the task performance of the human, as measured by psychophysical studies, and hence to serve as the basis for optimization of image quality. In this paper, we consider the task of detection of a weak signal in a noisy image. The mathematical observers considered include the ideal Bayesian, the nonprewhitening matched filter, a model based on linear-discriminant analysis and referred to as the Hotelling observer, and the Hotelling and Bayesian observers modified to account for the spatial-frequency-selective channels in the human visual system. The theory behind these observer models is briefly reviewed, and several psychophysical studies relating to the choice among them are summarized. Only the Hotelling model with channels is mathematically tractable in all cases considered here and capable of accounting for all of these data. This model requires no adjustment of parameters to fit the data and is relatively insensitive to the details of the channel mechanism. We therefore suggest it as a useful model observer for the purpose of assessing and optimizing image quality with respect to simple detection tasks.
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