Ideal versus human observer for long-tailed point spread functions: does deconvolution help?

The ideal observer represents a Bayesian approach to performing detection tasks. Since such tasks are frequently used as a prototype tasks for radiological imaging systems, the detectability measured at the output of an ideal detector can be used as a figure of merit to characterize the imaging system. For the detectability achieved by the ideal observer to be a good figure of merit, it should predict the ability of the human observer to perform the same detection task. Of great general interest, especially to the medical community, are imaging devices with long-tailed point spread functions (PSFs). Such PSFs may occur due to septal penetration in collimators, veiling glare in image intensifiers or scattered radiation in the body. We have investigated the effect that this type of PSF has on human visual signal detection and whether any improvement in performance can be gained by deconvolving the tails of the PSF. For the ideal observer, it is straightforward to show that the performance is independent of any linear, invertible deconvolution filter. Our psychophysical studies show, however, that performance of the human observer is indeed improved by deconvolution. The ideal observer is, therefore, not a good predictor of human observer performance for detection of a signal imaged through a long-tailed PSF. We offer some explanations for this discrepancy by using some characteristics of the visual process and suggest a standard of comparison for the human observer that takes into account these characteristics. A look at the performance of the non-prewhitening (npw) ideal observer, before and after deconvolution, also brings some good insight into this study.