Bayesian sparsity and class sparsity priors for dictionary learning and coding

TL;DR

This paper introduces a Bayesian framework for dictionary learning that compresses and deflates dictionaries to improve computational efficiency and accuracy in inverse problems like glitch detection and remote sensing.

Contribution

It proposes a novel Bayesian workflow that handles dictionary compression errors and employs group sparsity to identify relevant subdictionaries, enhancing matching efficiency.

Findings

Significant reduction in computational complexity.

Effective handling of dictionary compression errors.

Successful application to real-world problems like LIGO glitch detection.

Abstract

Dictionary learning methods continue to gain popularity for the solution of challenging inverse problems. In the dictionary learning approach, the computational forward model is replaced by a large dictionary of possible outcomes, and the problem is to identify the dictionary entries that best match the data, akin to traditional query matching in search engines. Sparse coding techniques are used to guarantee that the dictionary matching identifies only few of the dictionary entries, and dictionary compression methods are used to reduce the complexity of the matching problem. In this article, we propose a work flow to facilitate the dictionary matching process. First, the full dictionary is divided into subdictionaries that are separately compressed. The error introduced by the dictionary compression is handled in the Bayesian framework as a modeling error. Furthermore, we propose a new Bayesian data-driven group sparsity coding method to help identify subdictionaries that are not relevant for the dictionary matching. After discarding irrelevant subdictionaries, the dictionary matching is addressed as a deflated problem using sparse coding. The compression and deflation steps can lead to substantial decreases of the computational complexity. The effectiveness of compensating for the dictionary compression error and using the novel group sparsity promotion to deflate the original dictionary are illustrated by applying the methodology to real world problems, the glitch detection in the LIGO experiment and hyperspectral remote sensing.