Gaussian-Cauchy mixture modeling for robust signal-dependent noise estimation

We introduce an adaptive Gaussian-Cauchy mixture modeling for the likelihood of pairwise mean/standard-deviation scatter points found when estimating signal-dependent noise. The maximization of the likelihood is used to identify the noise-model parameters, following an adaptive mixture parameter that controls the balance between the Gaussian and the heavy-tailed Cauchy. This renders the estimation robust with respect to outliers, typically present in large quantities among the scatter points from images dominated by texture. The modeling is directly suited to describing also observations subject to clipping, i.e. under- or over-exposure. Experiments on a dataset of badly exposed and highly textured images demonstrate the effectiveness of the adaptive Gaussian-Cauchy mixture likelihood for the accurate estimation of the noise standard-deviation curve.