A comparison of sparse Bayesian regularization methods on computed tomography reconstruction

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23220%2F18%3A43951832" target="_blank" >RIV/49777513:23220/18:43951832 - isvavai.cz</a>

Výsledek na webu

<a href="http://iopscience.iop.org/article/10.1088/1742-6596/1047/1/012013/meta" target="_blank" >http://iopscience.iop.org/article/10.1088/1742-6596/1047/1/012013/meta</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1742-6596/1047/1/012013" target="_blank" >10.1088/1742-6596/1047/1/012013</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A comparison of sparse Bayesian regularization methods on computed tomography reconstruction

Popis výsledku v původním jazyce

Design of regularization term is an important part of solution of an ill-posed linear inverse problem. Another important issue is selection of tuning parameters of the regularization term. We address this problem using Bayesian approach which treats tuning parameters as unknowns and estimates them from the data. Specifically, we study a regularization model known as Automatic Relevance Determination (ARD) and several methods of its solution. The first approach is the conventional Variational Bayes method using the symmetrical factorization of the posterior of the vector of unknowns and the vector of tuning parameters. The second approach is based on the idea of marginalization over the vector of unknowns or the vector of tuning parameters, while the complementary vector is estimated using maximum likelihood. The resulting algorithm is thus an optimization task with non-convex objective function, which is solved using standard gradient methods. The proposed algorithms are tested on real tomographic X-ray data and the comparison with conventional regularization techniques (Tikhonov and Lasso) is performed. The algorithm using marginalization over the tuning parameter is found to be closest to the ground truth with acceptable computational cost. MATLAB®implementation of the reconstruction algorithms is freely available for download.

Název v anglickém jazyce

A comparison of sparse Bayesian regularization methods on computed tomography reconstruction

Popis výsledku anglicky

Design of regularization term is an important part of solution of an ill-posed linear inverse problem. Another important issue is selection of tuning parameters of the regularization term. We address this problem using Bayesian approach which treats tuning parameters as unknowns and estimates them from the data. Specifically, we study a regularization model known as Automatic Relevance Determination (ARD) and several methods of its solution. The first approach is the conventional Variational Bayes method using the symmetrical factorization of the posterior of the vector of unknowns and the vector of tuning parameters. The second approach is based on the idea of marginalization over the vector of unknowns or the vector of tuning parameters, while the complementary vector is estimated using maximum likelihood. The resulting algorithm is thus an optimization task with non-convex objective function, which is solved using standard gradient methods. The proposed algorithms are tested on real tomographic X-ray data and the comparison with conventional regularization techniques (Tikhonov and Lasso) is performed. The algorithm using marginalization over the tuning parameter is found to be closest to the ground truth with acceptable computational cost. MATLAB®implementation of the reconstruction algorithms is freely available for download.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

20201 - Electrical and electronic engineering

Projekt

<a href="/cs/project/LO1607" target="_blank" >LO1607: RICE – Nové technologie a koncepce pro inteligentní průmyslové systémy</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Journal of Physics: Conference Series; 1047

ISBN

—

ISSN

1742-6588

e-ISSN

1742-6596

Počet stran výsledku

17

Strana od-do

1-17

Název nakladatele

IOP Publishing Ltd.

Místo vydání

Bristol

Místo konání akce

Waterloo, Canada

Datum konání akce

23. 5. 2017

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

—