Open Access Te Herenga Waka-Victoria University of Wellington
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Applications of a Bayesian Approach with Deep Learning to Solving Inverse Problems

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posted on 2022-08-10, 09:07 authored by Alexander, Peter

Inverse problems are among the most challenging and widespread problems in science today. Inverse problems are commonly ill-conditioned, having potentially infinitely many solutions, and prior assumptions must be made in order to make the solution unique. Techniques for solving inverse problems are typically bespoke, requiring different tools and frameworks for each problem.

In this thesis we use Bayes' rule as a generic solution to a range of inverse problems, coupled with the deep learning technique known as normalising flows to provide models for the prior. Bayes' provides great flexibility -- being easily applicable to a range of inverse problems -- as well as results competitive with, or even exceeding, state-of-the-art techniques in image reconstruction, MRI acceleration and radio astronomy.

History

Copyright Date

2022-08-10

Date of Award

2022-08-10

Publisher

Te Herenga Waka—Victoria University of Wellington

Rights License

CC BY-SA 4.0

Degree Discipline

Computer Science

Degree Grantor

Te Herenga Waka—Victoria University of Wellington

Degree Level

Masters

Degree Name

Master of Science

ANZSRC Socio-Economic Outcome code

280115 Expanding knowledge in the information and computing sciences

ANZSRC Type Of Activity code

1 Pure basic research

Victoria University of Wellington Item Type

Awarded Research Masters Thesis

Language

en_NZ

Victoria University of Wellington School

School of Engineering and Computer Science

Advisors

Teal, Paul