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 language | English |
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Title of host publication | 2019 27th European Signal Processing Conference (EUSIPCO) |
Publisher | IEEE |
ISBN (Electronic) | 9789082797039 |
DOIs | |
Publication status | Published - 18 Nov 2019 |
Event | 27th European Signal Processing Conference 2019 - A Coruna, Spain, A Coruna, Spain Duration: 2 Sept 2019 → 7 Sept 2019 http://eusipco2019.org/ |
Publication series
Name | European Signal Processing Conference |
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ISSN (Print) | 2219-5491 |
Conference
Conference | 27th European Signal Processing Conference 2019 |
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Abbreviated title | EUSIPCO |
Country/Territory | Spain |
City | A Coruna |
Period | 2/09/19 → 7/09/19 |
Internet address |
Keywords
- Bayesian inference
- Convex optimisation
- Image/signal processing
- Inverse problem
- Uncertainty quantification
ASJC Scopus subject areas
- Signal Processing
- Electrical and Electronic Engineering