Optimal templates for signal extraction by noisy ideal detectors and human observers

The optimal template for signal detection in white additive noise is the signal itself: the ideal observer matches each stimulus against this template and selects the stimulus associated with largest match. In the noisy ideal observer, internal noise is added to the decision variable returned by the template. While the ideal observer represents an unrealistic approximation to the human visual process, the noisy ideal observer may be applicable under certain experimental conditions. For template values constrained to lie within a specified range, theory predicts that the template associated with a noisy ideal observer should be a clipped image of the signal, a result which we demonstrate analytically using variational calculus. It is currently unknown whether the human process conforms to theory. We report a targeted analysis of the theoretical prediction for an experimental protocol that maximizes template-matching on the part of human participants. We find indicative evidence to support the theoretical expectation when internal noise is compared across participants, but not within each participant. Our results indicate that implicit knowledge about internal variability in different individuals is reflected by their detection templates; no implicit knowledge is retained for internal-noise fluctuations experienced by a given participant during data collection. The results also indicate that template encoding is constrained by the dynamic range of weight specification, rather than the range of output values transduced by the template-matching process.