"Two prior models for edge-preserving Bayesian inversion" & "Geometry Parameter Estimation for Sparse X-ray Log Imaging"
Felipe Uribe & Angelina Senchukova, LUT University, Finland Campus Golm, building 9, room 1.2210:15 - 11:15
Abstract by Felipe Uribe:
In inverse problems arising in imaging science characterization of sharp edges in the solution is desired. Within the Bayesian approach to these problems, edge-preservation is often achieved using Markov random field (MRF) priors based on heavy-tailed distributions. Another strategy, popular in sparse statistics, is the application of hierarchical shrinkage priors. In this presentation, we revisit two models from each category, namely, the Laplace MRF and horseshoe priors. Moreover, we discuss a Gibbs sampling framework to solve the associated Bayesian inverse problems. Deconvolution and tomography applications are used to illustrate each of the prior models.
Abstract by Angelina Senchukova:
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.