Frequentist and Bayesian inference for Gaussian-log-Gaussian wavelet trees, and statistical signal processing applications

TL;DR

This paper introduces new estimation methods for Gaussian scale mixture models in wavelet trees, utilizing modern composite likelihood and Bayesian inference techniques, with applications in image denoising and edge detection.

Contribution

It presents novel estimation approaches for Gaussian-log-Gaussian wavelet trees based on composite likelihoods and approximate Bayesian inference, advancing statistical signal processing methods.

Findings

Effective denoising of 2D images demonstrated

Improved edge detection results shown

Method outperforms traditional approaches

Abstract

We introduce new estimation methods for a sub-class of the Gaussian scale mixture models for wavelet trees by Wainwright, Simoncelli & Willsky that rely on modern results for composite likelihoods and approximate Bayesian inference. Our methodology is illustrated for denoising and edge detection problems in two-dimensional images.