https://doi.org/10.1140/epjp/s13360-024-05394-7
Regular Article
Randomized recursive techniques for image reconstruction in diffuse optical tomography
1
Department of Electronics and Communication Engineering, National Institute of Technology, 403401, Goa, India
2
Department of Applied Science, National Institute of Technology, 403401, Goa, India
Received:
15
December
2023
Accepted:
24
June
2024
Published online:
5
July
2024
The inverse problem of reconstructing images in diffuse optical tomography poses significant challenges as it is characterized by high nonlinearity, under-determined, and an ill-posed nature. The conventional procedure applied to address this challenge is the Levenberg–Marquardt technique, which estimates updates for the variables (or nodes) in the imaging domain sequentially and is acknowledged for generating low-quality reconstructed images. To enhance the stability of inverting the large-sized matrix, a regularization parameter is heuristically selected and employed, which is computationally expensive. In this study, randomized recursive methods such as Randomized Kaczmarz, Randomized Extended Kaczmarz and Randomized Extended Gauss–Seidel methods are introduced to address the diffuse optical tomography inverse problem. Notably, these methods do not rely on the estimation of regularization parameters or the construction and inversion of large Hessian matrices. These methods randomly select to update the optical property of a node in the imaging domain based on a probability distribution determined by the entries of the sensitivity/Jacobian matrix. They provide a stable solution efficiently, and their reconstruction performance is assessed in both 2- and 3-dimensional imaging scenarios under various noise levels, as well as with real-phantom data. The numerical and experimental results demonstrate that these randomized recursive methods are capable of effectively recovering the optical parameters in diffuse optical tomography.
Ravi Prasad K. Jagannath and Gurusiddappa R. Prashanth: These authors have contributed equally to this work.
The original online version of this article was revised: Fig. 5 has been updated.
A correction to this article is available online at https://doi.org/10.1140/epjp/s13360-024-05465-9.
Copyright comment corrected publication 2024
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. corrected publication 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
