Overcomplete tomography: a novel approach to imaging

Turunçtur, Buse; Valentine, Andrew; Sambridge, Malcolm

Abstract

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.

Citation

Turunçtur, B., Valentine, A., & Sambridge, M. (2023). Overcomplete tomography: a novel approach to imaging. RAS Techniques and Instruments, 2(1), 207-215. https://doi.org/10.1093/rasti/rzad010

• 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
• DOI: https://doi.org/10.1093/rasti/rzad010
• Keywords: algorithms, multiscale tomography, overcomplete basis, data methods, L 1-norm based inversion, model parametrization
• Public URL: https://durham-repository.worktribe.com/output/1716042