Large Scale Variational Bayesian Inference for Structured Scale Mixture Models

TL;DR

This paper introduces a large-scale variational Bayesian inference algorithm for hierarchical scale mixture models, significantly improving image denoising and inpainting by capturing complex dependencies beyond traditional factorial priors.

Contribution

It presents a novel scalable Bayesian inference method for non-factorial latent tree models, enhancing image processing tasks over existing factorial approaches.

Findings

Improved denoising and inpainting results over MAP and factorial priors.

Demonstrates the effectiveness of hierarchical priors in image models.

Provides a scalable inference algorithm for complex structured models.

Abstract

Natural image statistics exhibit hierarchical dependencies across multiple scales. Representing such prior knowledge in non-factorial latent tree models can boost performance of image denoising, inpainting, deconvolution or reconstruction substantially, beyond standard factorial "sparse" methodology. We derive a large scale approximate Bayesian inference algorithm for linear models with non-factorial (latent tree-structured) scale mixture priors. Experimental results on a range of denoising and inpainting problems demonstrate substantially improved performance compared to MAP estimation or to inference with factorial priors.