A Visually Adaptive Bayesian Model In Wavelet Regression

Abstract

The implementation of a Bayesian approach to wavelet regression that corresponds to the human visual system is examined. Most existing research in this area assumes non-informative priors, that is, a prior with mean zero. A new way is offered to implement prior information that mimics a visual inspection of noisy data, to obtain a first impression about the shape of the function that results in a prior with non-zero mean. This visually adaptive Bayesian (VAB) prior has a simple structure, intuitive interpretation, and is easy to implement. Skorohod topology is suggested as a more appropriate measure in signal recovering than the commonly used mean-squared error.