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Overcomplete tomography: a novel approach to imaging

Turunçtur, Buse; Valentine, Andrew; Sambridge, Malcolm

Overcomplete tomography: a novel approach to imaging Thumbnail


Buse Turunçtur

Malcolm Sambridge


Regularized least-squares tomography offers a straightforward and efficient imaging method and has seen extensive application across various fields. However, it has a few drawbacks, such as (i) the regularization imposed during the inversion tends to give a smooth solution, which will fail to reconstruct a multi-scale model well or detect sharp discontinuities, (ii) it requires finding optimum control parameters, and (iii) it does not produce a sparse solution. This paper introduces ‘overcomplete tomography’, a novel imaging framework that allows high-resolution recovery with relatively few data points. We express our image in terms of an overcomplete basis, allowing the representation of a wide range of features and characteristics. Following the insight of ‘compressive sensing’, we regularize our inversion by imposing a penalty on the L1 norm of the recovered model, obtaining an image that is sparse relative to the overcomplete basis. We demonstrate our method with a synthetic and a real X-ray tomography example. Our experiments indicate that we can reconstruct a multi-scale model from only a few observations. The approach may also assist interpretation, allowing images to be decomposed into (for example) ‘global’ and ‘local’ structures. The framework presented here can find application across a wide range of fields, including engineering, medical and geophysical tomography.


Turunçtur, B., Valentine, A., & Sambridge, M. (2023). Overcomplete tomography: a novel approach to imaging. RAS Techniques and Instruments, 2(1), 207-215.

Journal Article Type Article
Acceptance Date Mar 24, 2023
Online Publication Date Apr 28, 2023
Publication Date Jan 17, 2023
Deposit Date Aug 11, 2023
Publicly Available Date Aug 11, 2023
Journal RAS Techniques and Instruments
Print ISSN 2752-8200
Publisher Oxford University Press
Peer Reviewed Peer Reviewed
Volume 2
Issue 1
Pages 207-215
Keywords algorithms, multiscale tomography, overcomplete basis, data methods, L 1-norm based inversion, model parametrization
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Copyright Statement
© 2023 The Author(s)
Published by Oxford University Press on behalf of the Royal Astronomical SocietyThis is an Open Access article distributed under the terms of the Creative
Commons Attribution License ( http://cr eativecommons.or g/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium,
provided the original work is properly cited.

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