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

Stéphane Chrétien, Camille Giampiccolo, Wenjuan Sun and Jessica Talbott
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Stéphane Chrétien: Laboratoire ERIC, Université Lyon 2, 5 Av. Pierre Mendès-France, 69676 Bron, France
Camille Giampiccolo: Laboratoire de Mathématiques de Besançon, UFR Sciences et Techniques, University de Bourgogne Franche-Comté, 16 Route de Gray, CEDEX, 25030 Besançon, France
Wenjuan Sun: National Physical Laboratory, Hampton Road, Teddington TW11 0LW, UK
Jessica Talbott: National Physical Laboratory, Hampton Road, Teddington TW11 0LW, UK

Mathematics, 2021, vol. 9, issue 22, 1-12

Abstract: 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.

Keywords: XCT reconstruction; sparsity enforcing penalties; hyperparameter selection; Bayesian optimisation; virtual planted reference image (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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