Quantifying uncertainty in high dimensional inverse problems by convex optimisation

Xiaohao Cai, Marcelo Pereyra, Jason D. McEwen

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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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.

Original languageEnglish
Title of host publication2019 27th European Signal Processing Conference (EUSIPCO)
PublisherIEEE
ISBN (Electronic)9789082797039
DOIs
Publication statusPublished - 18 Nov 2019
Event27th European Signal Processing Conference 2019 - A Coruna, Spain, A Coruna, Spain
Duration: 2 Sep 20197 Sep 2019
http://eusipco2019.org/

Publication series

NameEuropean Signal Processing Conference
ISSN (Print)2219-5491

Conference

Conference27th European Signal Processing Conference 2019
Abbreviated titleEUSIPCO
CountrySpain
CityA Coruna
Period2/09/197/09/19
Internet address

Keywords

  • Bayesian inference
  • Convex optimisation
  • Image/signal processing
  • Inverse problem
  • Uncertainty quantification

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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  • Cite this

    Cai, X., Pereyra, M., & McEwen, J. D. (2019). Quantifying uncertainty in high dimensional inverse problems by convex optimisation. In 2019 27th European Signal Processing Conference (EUSIPCO) [8903038] (European Signal Processing Conference). IEEE. https://doi.org/10.23919/EUSIPCO.2019.8903038