A number of task-specific approaches to the assessment of image quality are treated. Both estimation and classification tasks are considered, but only linear estimators or classifiers are permitted. Performance on these tasks is limited by both quantum noise and object variability, and the effects of postprocessing or image-reconstruction algorithms are explicitly included. The results are expressed as signal-to-noise ratios (SNR's). The interrelationships among these SNR's are considered, and an SNR for a classification task is expressed as the SNR for a related estimation task times four factors. These factors show the effects of signal size and contrast, conspicuity of the signal, bias in the estimation task, and noise correlation. Ways of choosing and calculating appropriate SNR's for system evaluation and optimization are also discussed.