2023
DOI: 10.1137/21m1433782
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Uncertainty Quantification of Inclusion Boundaries in the Context of X-Ray Tomography

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Cited by 7 publications
(15 citation statements)
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References 43 publications
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“…However, such priors often result in a large set of parameters, yielding inefficient numerical uncertainty quantification methods for fine discretization levels. Recently, a new class of Bayesian priors has emerged where a discontinuous field is constructed using a non-linear transformation of a continuous prior [2,13,24]. A continuous prior can be constructed with a relatively few parameters, e.g.…”
Section: Cuqipy-fenics Example: Eitmentioning
confidence: 99%
“…However, such priors often result in a large set of parameters, yielding inefficient numerical uncertainty quantification methods for fine discretization levels. Recently, a new class of Bayesian priors has emerged where a discontinuous field is constructed using a non-linear transformation of a continuous prior [2,13,24]. A continuous prior can be constructed with a relatively few parameters, e.g.…”
Section: Cuqipy-fenics Example: Eitmentioning
confidence: 99%
“…Irregular boundaries are better represented by general radius functions r(θ), see [2,4]. In our case, we approximate the boundary by a piecewise linear reconstruction built on a uniform mesh θ j of [0, 1] with node values r j = r(θ j ), j = 0, .…”
Section: Inverse Problemmentioning
confidence: 99%
“…In our numerical tests, each block starts with (σ ℓ x ) 2 = (σ ℓ y ) 2 = 0.1 and ends with (σ µ ) 2 = 20 2 . Then (σ ℓ a0 ) 2 = 0.1 and (σ ℓ aq ) 2 = (σ ℓ bq ) 2 = 0.1/(1 + q 2 ) s , 1 ⩽ q ⩽ Q, s large, as in [9], so that the prior favors regular shapes with r(t) > 0.…”
Section: Prior Constructionmentioning
confidence: 99%
See 1 more Smart Citation
“…In this paper, we consider a Bayesian approach that captures this idea for two parametrizations used in detection of inclusions for nonlinear inverse problems: the star-shaped set and level set parametrizations. These parametrizations are studied rigorously in [9][10][11] and remain popular to Bayesian practitioners: we mention [1,[12][13][14][15][16] in the case of the star-shaped inclusions and [12,[17][18][19][20][21] for the level set inclusions, see also references therein.…”
Section: Introductionmentioning
confidence: 99%