Non-stationary multi-layered Gaussian priors for Bayesian inversion

Emzir, Muhammad F.; Lasanen, Sari; Purisha, Zenith; Roininen, Lassi; Särkkä, Simo

doi:10.1088/1361-6420/abc962

Cited by 11 publications

(9 citation statements)

References 52 publications

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“…The setup acts as a proof-of-concept for our detectors with respect to their performance as multispectral photoncounting devices. The exemplary tomographic spectrum-per-pixel data collected can be used as input to test a sophisticated reconstruction algorithm (work in progress [11,12]) to reconstruct the phantom as a multispectral image.…”

Section: Spectral Measurementsmentioning

confidence: 99%

Quality assessment of Cadmium Telluride as a detector material for multispectral medical imaging

Kirschenmann,

Bezak,

Bharthuar

et al. 2022

Preprint

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Cadmium Telluride (CdTe) is a high-Z material with excellent photon radiation absorption properties, making it a promising material to include in radiation detection technologies. However, the brittleness of CdTe crystals as well as their varying concentration of defects necessitate a thorough quality assessment before the complex detector processing procedure. We present our quality assessment of CdTe as a detector material for multispectral medical imaging, a research which is conducted as part of the Consortium Project Multispectral Photon-counting for Medical Imaging and Beam characterization (MPMIB). The aim of the project is to develop novel CdTe detectors and obtain spectrum-per-pixel information that make the distinction between different radiation types and tissues possible. To evaluate the defect density inside the crystals -which can deteriorate the detector performance -we employ infrared microscopy (IRM). Posterior data analysis allows us to visualise the defect distributions as 3D defect maps. Additionally, we investigate front and backside differences of the material with current-voltage (IV) measurements to determine the preferred surface for the pixelisation of the crystal, and perform test measurements with the prototypes to provide feedback for further processing. We present the different parts of our quality assessment chain and will close with first experimental results obtained with one of our prototype PC detectors in a small tomographic setup.

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Section: Spectral Measurementsmentioning

confidence: 99%

Quality assessment of Cadmium Telluride as a detector material for multispectral medical imaging

Kirschenmann,

Bezak,

Bharthuar

et al. 2022

Preprint

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“…Generalizing the temporal SS-DGPs to spatio-temporal SS-DGPs (see, the end of Section 4.2) would be worth studying as well, by extending the methodologies introduced in ; Emzir et al (2020).…”

Section: Real Data Application On Ligo Gravitational Wave Detectionmentioning

confidence: 99%

“…The idea of putting GP priors on the hyperpameters of a GP (Heinonen et al 2016;Roininen et al 2019;Salimbeni and Deisenroth 2017b) can be continued hierarchically, which leads to one type of deep Gaussian process (DGP) construction (Dunlop et al 2018;Emzir et al 2019Emzir et al , 2020. Namely, the GP is conditioned on another GP, which again depends on another GP, and so forth.…”

Section: Introductionmentioning

confidence: 99%

Deep state-space Gaussian processes

2021

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This paper is concerned with a state-space approach to deep Gaussian process (DGP) regression. We construct the DGP by hierarchically putting transformed Gaussian process (GP) priors on the length scales and magnitudes of the next level of Gaussian processes in the hierarchy. The idea of the state-space approach is to represent the DGP as a non-linear hierarchical system of linear stochastic differential equations (SDEs), where each SDE corresponds to a conditional GP. The DGP regression problem then becomes a state estimation problem, and we can estimate the state efficiently with sequential methods by using the Markov property of the state-space DGP. The computational complexity scales linearly with respect to the number of measurements. Based on this, we formulate state-space MAP as well as Bayesian filtering and smoothing solutions to the DGP regression problem. We demonstrate the performance of the proposed models and methods on synthetic non-stationary signals and apply the state-space DGP to detection of the gravitational waves from LIGO measurements.

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“…Recently, several hierarchical models, which promote more versatile behaviors, have been developed. These include, for example, deep Gaussian processes (Dunlop et al, 2018; Emzir et al, 2020), level-set methods (Dunlop et al, 2017), mixtures of compound Poisson processes and Gaussians (Hosseini, 2017), and stacked Matérn fields via stochastic partial differential equations (Roininen et al, 2019). The problem with hierarchical priors is that in the posteriors, the parameters and hyperparameters may become strongly coupled, which means that vanilla MCMC methods become problematic and, for example, reparameterizations are needed for sampling the posterior efficiently (Chada et al, 2019; Monterrubio-Gómez et al, 2020).…”

Section: Introductionmentioning

confidence: 99%

Enhancing industrial X-ray tomography by data-centric statistical methods

Suuronen

Emzir

Lasanen

et al. 2020

DCE

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X-ray tomography has applications in various industrial fields such as sawmill industry, oil and gas industry, as well as chemical, biomedical, and geotechnical engineering. In this article, we study Bayesian methods for the X-ray tomography reconstruction. In Bayesian methods, the inverse problem of tomographic reconstruction is solved with the help of a statistical prior distribution which encodes the possible internal structures by assigning probabilities for smoothness and edge distribution of the object. We compare Gaussian random field priors, that favor smoothness, to non-Gaussian total variation (TV), Besov, and Cauchy priors which promote sharp edges and high- and low-contrast areas in the object. We also present computational schemes for solving the resulting high-dimensional Bayesian inverse problem with 100,000–1,000,000 unknowns. We study the applicability of a no-U-turn variant of Hamiltonian Monte Carlo (HMC) methods and of a more classical adaptive Metropolis-within-Gibbs (MwG) algorithm to enable full uncertainty quantification of the reconstructions. We use maximum a posteriori (MAP) estimates with limited-memory BFGS (Broyden–Fletcher–Goldfarb–Shanno) optimization algorithm. As the first industrial application, we consider sawmill industry X-ray log tomography. The logs have knots, rotten parts, and even possibly metallic pieces, making them good examples for non-Gaussian priors. Secondly, we study drill-core rock sample tomography, an example from oil and gas industry. In that case, we compare the priors without uncertainty quantification. We show that Cauchy priors produce smaller number of artefacts than other choices, especially with sparse high-noise measurements, and choosing HMC enables systematic uncertainty quantification, provided that the posterior is not pathologically multimodal or heavy-tailed.

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Non-stationary multi-layered Gaussian priors for Bayesian inversion

Cited by 11 publications

References 52 publications

Quality assessment of Cadmium Telluride as a detector material for multispectral medical imaging

Quality assessment of Cadmium Telluride as a detector material for multispectral medical imaging

Deep state-space Gaussian processes

Enhancing industrial X-ray tomography by data-centric statistical methods

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