Cauchy Markov random field priors for Bayesian inversion

Chada, Neil K.; Roininen, Lassi; Suuronen, Jarkko

doi:10.1007/s11222-022-10089-z

Cited by 13 publications

(15 citation statements)

References 51 publications

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“…Finally, we consider the sparse-angle tomography and employ maximum a posteriori estimates with recently developed class of priors, firstorder isotropic Cauchy difference priors [24]. We demonstrate the amenability, for our specific use case, of this method over conventional methods (filtered backprojection, Tikhonov regularisation) when the number of projection data is extremely limited.…”

Section: Our Contributionsmentioning

confidence: 96%

“…Employing Cauchy distribution for the distribution of the differences effectively allows the existence of discontinuities in x by favouring features that are piecewise close to constant. These characteristics of the Cauchy difference prior are notably different compared to Gaussian difference priors and most other non-deep Gaussian random field priors due to the infinite variance of the Cauchy distribution [24]. We do not claim that the Cauchy difference prior is superior to Gaussian or other random field priors in log tomography in terms of reconstruction capabilities, but instead we use the Cauchy difference prior as an optional reconstruction tool due to its simplicity and unique features.…”

Section: Bayesian Inversion With Cauchy Priormentioning

confidence: 96%

“…As the third image reconstruction method, we employ the maximum a posteriori (MAP) estimate of the posterior distribution with the first-order isotropic Cauchy difference prior [24,28,29] and the following data likelihood term…”

Section: Bayesian Inversion With Cauchy Priormentioning

confidence: 99%

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Geometry Parameter Estimation for Sparse X-ray Log Imaging

Senchukova

Suuronen

Heikkinen³

et al. 2022

Preprint

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We consider geometry parameter estimation in industrial sawmill fan-beam X-ray tomography. In such industrial settings, scanners do not always allow identification of the location of the source-detector pair, which creates the issue of unknown geometry. This work considers two approaches for geometry estimation. Our first approach is a calibration object correlation method in which we calculate the maximum cross-correlation between a known-sized calibration object image and its filtered backprojection reconstruction and use differential evolution as an optimiser. The second approach is projection trajectory simulation, where we use a set of known intersection points and a sequential Monte Carlo method for estimating the posterior density of the parameters. We show numerically that a large set of parameters can be used for artefact-free reconstruction. We deploy Bayesian inversion with Cauchy priors for synthetic and real sawmill data for detection of knots with a very low number of measurements and uncertain measurement geometry.

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Section: Our Contributionsmentioning

confidence: 96%

Section: Bayesian Inversion With Cauchy Priormentioning

confidence: 96%

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Geometry Parameter Estimation for Sparse X-ray Log Imaging

Senchukova

Suuronen

Heikkinen³

et al. 2022

Preprint

Self Cite

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“…where Λ(τ, w) is given in (12). Given the hyperparameters σ obs , τ and w, the most common sampling algorithm for a Gaussian distribution is based on the Cholesky factorization.…”

Section: Sampling Of πmentioning

confidence: 99%

“…The idea is to increase the probability of large jump events by imposing heavy-tailed distributions on the increments. Some examples include total variation prior [10], Laplace Markov random fields [11,8] and Cauchy Markov random fields [12].…”

Section: Introductionmentioning

confidence: 99%

Horseshoe priors for edge-preserving linear Bayesian inversion

Uribe¹,

Dong²,

Hansen³

2022

Preprint

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In many large-scale inverse problems, such as computed tomography and image deblurring, characterization of sharp edges in the solution is desired. Within the Bayesian approach to inverse problems, edgepreservation is often achieved using Markov random field priors based on heavy-tailed distributions. Another strategy, popular in statistics, is the application of hierarchical shrinkage priors. An advantage of this formulation lies in expressing the prior as a conditionally Gaussian distribution depending of global and local hyperparameters which are endowed with heavy-tailed hyperpriors. In this work, we revisit the shrinkage horseshoe prior and introduce its formulation for edge-preserving settings. We discuss a sampling framework based on the Gibbs sampler to solve the resulting hierarchical formulation of the Bayesian inverse problem. In particular, one of the conditional distributions is high-dimensional Gaussian, and the rest are derived in closed form by using a scale mixture representation of the heavy-tailed hyperpriors. Applications from imaging science show that our computational procedure is able to compute sharp edge-preserving posterior point estimates with reduced uncertainty.

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Spatial Field

Bolin¹

2022

Wiley StatsRef: Statistics Reference Online

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Spatial fields, aka random fields, are important models for analyzing data collected at different spatial locations. This article provides a short introduction to spatial fields for continuously indexed data, focusing on how to construct flexible Gaussian and non‐Gaussian fields. A brief introduction to spatial prediction of random fields is given, and approaches for dealing with the computational problems that arise when using spatial fields to analyze large data sets are discussed.

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Cauchy Markov random field priors for Bayesian inversion

Cited by 13 publications

References 51 publications

Geometry Parameter Estimation for Sparse X-ray Log Imaging

Geometry Parameter Estimation for Sparse X-ray Log Imaging

Horseshoe priors for edge-preserving linear Bayesian inversion

Spatial Field

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