Gaussian-log-Gaussian wavelet trees, frequentist and Bayesian inference, and statistical signal processing applications
Jesper Michael Moller, Robert Dahl Jacobsen · arXiv (Cornell University) · 2014
We introduce a promising alternative to the usual hidden Markov tree model for Gaussian wavelet coefficients, where their variances are specified by the hidden states and take values in a finite set. In our new model, the hidden states have a similar dependence structure but they are jointly Gaussian, and the wavelet coefficients have log-variances equal to the hidden states. We argue why this provides a flexible model where frequentist and Bayesian inference procedures become tractable for estimation of parameters and hidden states. Our methodology is illustrated for denoising and edge detection problems in two-dimensional images.