Generalized sparse Bayesian learning and application to image reconstruction

TL;DR

This paper introduces a generalized sparse Bayesian learning framework that enhances image reconstruction by providing uncertainty quantification and adaptability across various data types and prior models.

Contribution

It presents a versatile Bayesian approach applicable to different imaging problems, overcoming limitations of existing methods tailored to specific models.

Findings

Potential for improved denoising and deblurring

Applicability to magnetic resonance imaging

Enhanced robustness and uncertainty quantification

Abstract

Image reconstruction based on indirect, noisy, or incomplete data remains an important yet challenging task. While methods such as compressive sensing have demonstrated high-resolution image recovery in various settings, there remain issues of robustness due to parameter tuning. Moreover, since the recovery is limited to a point estimate, it is impossible to quantify the uncertainty, which is often desirable. Due to these inherent limitations, a sparse Bayesian learning approach is sometimes adopted to recover a posterior distribution of the unknown. Sparse Bayesian learning assumes that some linear transformation of the unknown is sparse. However, most of the methods developed are tailored to specific problems, with particular forward models and priors. Here, we present a generalized approach to sparse Bayesian learning. It has the advantage that it can be used for various types of data acquisitions and prior information. Some preliminary results on image reconstruction/recovery indicate its potential use for denoising, deblurring, and magnetic resonance imaging.