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Quantifying uncertainty in high dimensional inverse problems by convex optimisation

Quantifying uncertainty in high dimensional inverse problems by convex optimisation
Quantifying uncertainty in high dimensional inverse problems by convex optimisation
Inverse problems play a key role in modern image/signal processing methods. However, since they are generally ill-conditioned or ill-posed due to lack of observations, their solutions may have significant intrinsic uncertainty. Analysing and quantifying this uncertainty is very challenging, particularly in high-dimensional problems and problems with non-smooth objective functionals (e.g. sparsity-promoting priors). In this article, a series of strategies to visualise this uncertainty are presented, e.g. highest posterior density credible regions, and local credible intervals (cf. error bars) for individual pixels and superpixels. Our methods support non-smooth priors for inverse problems and can be scaled to high-dimensional settings. Moreover, we present strategies to automatically set regularisation parameters so that the proposed uncertainty quantification (UQ) strategies become much easier to use. Also, different kinds of dictionaries (complete and over-complete) are used to represent the image/signal and their performance in the proposed UQ methodology is investigated.
Bayesian inference, Convex optimisation, Image/signal processing, Inverse problem, Uncertainty quantification
IEEE
Cai, Xiaohao
de483445-45e9-4b21-a4e8-b0427fc72cee
Pereyra, Marcelo
7ae249d9-94ea-4f67-a3ec-e2907665952e
McEwen, Jason D.
64c6269a-fe40-41d7-8b0c-d3c9ad920175
Cai, Xiaohao
de483445-45e9-4b21-a4e8-b0427fc72cee
Pereyra, Marcelo
7ae249d9-94ea-4f67-a3ec-e2907665952e
McEwen, Jason D.
64c6269a-fe40-41d7-8b0c-d3c9ad920175

Cai, Xiaohao, Pereyra, Marcelo and McEwen, Jason D. (2019) Quantifying uncertainty in high dimensional inverse problems by convex optimisation. In, 2019 27th European Signal Processing Conference (EUSIPCO). (European Signal Processing Conference, , (doi:10.23919/EUSIPCO.2019.8903038), 2019-September) IEEE. (doi:10.23919/EUSIPCO.2019.8903038).

Record type: Book Section

Abstract

Inverse problems play a key role in modern image/signal processing methods. However, since they are generally ill-conditioned or ill-posed due to lack of observations, their solutions may have significant intrinsic uncertainty. Analysing and quantifying this uncertainty is very challenging, particularly in high-dimensional problems and problems with non-smooth objective functionals (e.g. sparsity-promoting priors). In this article, a series of strategies to visualise this uncertainty are presented, e.g. highest posterior density credible regions, and local credible intervals (cf. error bars) for individual pixels and superpixels. Our methods support non-smooth priors for inverse problems and can be scaled to high-dimensional settings. Moreover, we present strategies to automatically set regularisation parameters so that the proposed uncertainty quantification (UQ) strategies become much easier to use. Also, different kinds of dictionaries (complete and over-complete) are used to represent the image/signal and their performance in the proposed UQ methodology is investigated.

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More information

Published date: 1 September 2019
Keywords: Bayesian inference, Convex optimisation, Image/signal processing, Inverse problem, Uncertainty quantification

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Local EPrints ID: 438749
URI: http://eprints.soton.ac.uk/id/eprint/438749
PURE UUID: 044ffdfc-975c-4b52-af9a-c894db76aef2

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Date deposited: 23 Mar 2020 18:43
Last modified: 19 May 2020 17:03

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Contributors

Author: Xiaohao Cai
Author: Marcelo Pereyra
Author: Jason D. McEwen

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