Estimation of linear observer templates in the presence of multi-peaked Gaussian noise through 2AFC experiments

We extend a method for linear template estimation developed by Abbey et al. which demonstrated that a linear observer template can be estimated effectively through a two-alternative forced choice (2AFC) experiment, assuming the noise in the images is Gaussian, or multivariate normal (MVN). We relax this assumption, allowing the noise in the images to be drawn from a weighted sum of MVN distributions, which we call a multi-peaked MVN (MPMVN) distribution. Our motivation is that more complicated probability density functions might be approximated in general by such MPMVN distributions. Our extension of Abbey et al.'s method requires us to impose the additional constraint that the covariance matrices of the component peaks of the signal-present noise distribution all be equal, and that the covariance matrices of the component peaks of the signal-absent noise distribution all be equal (but different in general from the signal-present covariance matrices). Preliminary research shows that our generalized method is capable of producing unbiased estimates of linear observer templates in the presence of MPMVN noise under the stated assumptions. We believe this extension represents a next step toward the general treatment of arbitrary image noise distributions.