Fast Hyperparameter Calibration of Sparsity Enforcing Penalties in Total Generalised Variation Penalised Reconstruction Methods for XCT Using a Planted Virtual Reference Image

The reconstruction problem in X-ray computed tomography (XCT) is notoriously difficult in the case where only a small number of measurements are made. Based on the recently discovered Compressed Sensing paradigm, many methods have been proposed in order to address the reconstruction problem by lever...

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Autores principales:	Stéphane Chrétien, Camille Giampiccolo, Wenjuan Sun, Jessica Talbott
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	XCT reconstruction sparsity enforcing penalties hyperparameter selection Bayesian optimisation virtual planted reference image Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/733437f6dba0467bbaad331145c0e46a
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spelling	oai:doaj.org-article:733437f6dba0467bbaad331145c0e46a2021-11-25T18:17:35ZFast Hyperparameter Calibration of Sparsity Enforcing Penalties in Total Generalised Variation Penalised Reconstruction Methods for XCT Using a Planted Virtual Reference Image10.3390/math92229602227-7390https://doaj.org/article/733437f6dba0467bbaad331145c0e46a2021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2960https://doaj.org/toc/2227-7390The reconstruction problem in X-ray computed tomography (XCT) is notoriously difficult in the case where only a small number of measurements are made. Based on the recently discovered Compressed Sensing paradigm, many methods have been proposed in order to address the reconstruction problem by leveraging inherent sparsity of the object’s decompositions in various appropriate bases or dictionaries. In practice, reconstruction is usually achieved by incorporating weighted sparsity enforcing penalisation functionals into the least-squares objective of the associated optimisation problem. One such penalisation functional is the Total Variation (TV) norm, which has been successfully employed since the early days of Compressed Sensing. Total Generalised Variation (TGV) is a recent improvement of this approach. One of the main advantages of such penalisation based approaches is that the resulting optimisation problem is convex and as such, cannot be affected by the possible existence of spurious solutions. Using the TGV penalisation nevertheless comes with the drawback of having to tune the two hyperparameters governing the TGV semi-norms. In this short note, we provide a simple and efficient recipe for fast hyperparameters tuning, based on the simple idea of virtually planting a mock image into the model. The proposed trick potentially applies to all linear inverse problems under the assumption that relevant prior information is available about the sought for solution, whilst being very different from the Bayesian method.Stéphane ChrétienCamille GiampiccoloWenjuan SunJessica TalbottMDPI AGarticleXCT reconstructionsparsity enforcing penaltieshyperparameter selectionBayesian optimisationvirtual planted reference imageMathematicsQA1-939ENMathematics, Vol 9, Iss 2960, p 2960 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	XCT reconstruction sparsity enforcing penalties hyperparameter selection Bayesian optimisation virtual planted reference image Mathematics QA1-939
spellingShingle	XCT reconstruction sparsity enforcing penalties hyperparameter selection Bayesian optimisation virtual planted reference image Mathematics QA1-939 Stéphane Chrétien Camille Giampiccolo Wenjuan Sun Jessica Talbott Fast Hyperparameter Calibration of Sparsity Enforcing Penalties in Total Generalised Variation Penalised Reconstruction Methods for XCT Using a Planted Virtual Reference Image
description	The reconstruction problem in X-ray computed tomography (XCT) is notoriously difficult in the case where only a small number of measurements are made. Based on the recently discovered Compressed Sensing paradigm, many methods have been proposed in order to address the reconstruction problem by leveraging inherent sparsity of the object’s decompositions in various appropriate bases or dictionaries. In practice, reconstruction is usually achieved by incorporating weighted sparsity enforcing penalisation functionals into the least-squares objective of the associated optimisation problem. One such penalisation functional is the Total Variation (TV) norm, which has been successfully employed since the early days of Compressed Sensing. Total Generalised Variation (TGV) is a recent improvement of this approach. One of the main advantages of such penalisation based approaches is that the resulting optimisation problem is convex and as such, cannot be affected by the possible existence of spurious solutions. Using the TGV penalisation nevertheless comes with the drawback of having to tune the two hyperparameters governing the TGV semi-norms. In this short note, we provide a simple and efficient recipe for fast hyperparameters tuning, based on the simple idea of virtually planting a mock image into the model. The proposed trick potentially applies to all linear inverse problems under the assumption that relevant prior information is available about the sought for solution, whilst being very different from the Bayesian method.
format	article
author	Stéphane Chrétien Camille Giampiccolo Wenjuan Sun Jessica Talbott
author_facet	Stéphane Chrétien Camille Giampiccolo Wenjuan Sun Jessica Talbott
author_sort	Stéphane Chrétien
title	Fast Hyperparameter Calibration of Sparsity Enforcing Penalties in Total Generalised Variation Penalised Reconstruction Methods for XCT Using a Planted Virtual Reference Image
title_short	Fast Hyperparameter Calibration of Sparsity Enforcing Penalties in Total Generalised Variation Penalised Reconstruction Methods for XCT Using a Planted Virtual Reference Image
title_full	Fast Hyperparameter Calibration of Sparsity Enforcing Penalties in Total Generalised Variation Penalised Reconstruction Methods for XCT Using a Planted Virtual Reference Image
title_fullStr	Fast Hyperparameter Calibration of Sparsity Enforcing Penalties in Total Generalised Variation Penalised Reconstruction Methods for XCT Using a Planted Virtual Reference Image
title_full_unstemmed	Fast Hyperparameter Calibration of Sparsity Enforcing Penalties in Total Generalised Variation Penalised Reconstruction Methods for XCT Using a Planted Virtual Reference Image
title_sort	fast hyperparameter calibration of sparsity enforcing penalties in total generalised variation penalised reconstruction methods for xct using a planted virtual reference image
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/733437f6dba0467bbaad331145c0e46a
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Fast Hyperparameter Calibration of Sparsity Enforcing Penalties in Total Generalised Variation Penalised Reconstruction Methods for XCT Using a Planted Virtual Reference Image

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