Optimal shifted estimates of human-observer templates in two-alternative forced-choice experiments

For performing simple detection and discrimination tasks in image noise, human observers are often modeled by a cross-correlation between the image and an observer template followed by the injection of the observer's internal noise. This paper is concerned with estimating this template using the two-alternative forced-choice (2AFC) experimental paradigm. The basic idea behind the estimation procedure is to average the noise fields of the images used in a 2AFC experiment with a weight that depends on whether the observer got the trial correct or incorrect. We describe a method that produces unbiased estimates of the observer template up to a constant of proportionality under the linear cross-correlation model. The method proposed here is different from some previous methods in the way it assigns weights to the noise fields and we show that the resulting errors in the estimated template are minimized. We also propose and validate a formula for approximating the error covariance associated with the template estimates.