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Generalized Sparse Bayesian Learning and Application to Image Reconstruction
Department of Mathematics, Dartmouth College, Hanover, NH, USA..ORCID iD: 0000-0002-3434-5563
Department of Mathematics, Dartmouth College, Hanover, NH 03755 USA..
Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529 USA..
2023 (English)In: SIAM/ASA Journal on Uncertainty Quantification, E-ISSN 2166-2525, Vol. 11, no 1, p. 262-284Article in journal (Refereed) Published
Abstract [en]

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 imagerecovery 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 issometimes adopted to recover a posterior distribution of the unknown. Sparse Bayesian learningassumes 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 beused for various types of data acquisitions and prior information. Some preliminary results on imagereconstruction/recovery indicate its potential use for denoising, deblurring, and magnetic resonanceimaging.

Place, publisher, year, edition, pages
2023. Vol. 11, no 1, p. 262-284
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-218032DOI: 10.1137/22m147236xOAI: oai:DiVA.org:liu-218032DiVA, id: diva2:2000303
Available from: 2025-09-23 Created: 2025-09-23 Last updated: 2026-01-09

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