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2024 | OriginalPaper | Chapter

Comparison Between Gradient Descent and Adam Algorithms for Image Reconstruction in Diffuse Optical Tomography

Authors : Nada Chakhim, Mohamed Louzar, Abdellah Lamnii, Mohammed Alaoui

Published in: Applied Mathematics and Modelling in Finance, Marketing and Economics

Publisher: Springer Nature Switzerland

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Abstract

In this work, we aim to solve the inverse problem of diffuse optical tomography by using enhanced gradient descent methods. The light propagation throughout the medium is described by the diffusion approximation in frequency domain. For comparison purpose we use the gradient descent method. We have studied the convergence of the objective functional. Our simulation results, in all cases we have tested, show the robustness and the quick convergence of Adam algorithm compared to the gradient descent algorithm.

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Literature
1.
Gopinath, S., Robertson, C.S., Grossman, R.G., Chance, B.: Near-infrared spectroscopic localization of intracranial hematomas. J. Neurosurg. 79, 43–47 (1993)CrossRef
2.
Taroni, P., et al.: Noninvasive assessment of breast cancer risk using time-resolved diffuse optical spectroscopy. J. Biomed. Opt. 15(6), 060501 (2010)CrossRef
3.
Klose, A.D., Hielscher: Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer. Med. Phys. (1999)
4.
Arridge, S.R., Schotland, J.C.: Optical tomography: forward and inverse problems. In: Inverse Problems (2009)
5.
Roy, R., Sevick-Muraca, E.M.: A numerical study of gradient based nonlinear optimization methods for contrast enhanced optical tomography. Opt. Express 9(1), 49–65 (2001)CrossRef
6.
7.
Kingma, D.P., Lei Ba, J.: Adam: a method for stochastic optimization. In: Conference Paper at ICLR (2015)
8.
Ruder, S.: An overview of gradient descent optimization algorithms (2017)
9.
Henyey, L.C., Greenstein, J.L.: Diffuse radiation in the galaxy. Astrophys. J. 93, 70–83 (1941)CrossRef
10.
Arridge, S.R., Schweiger, M., Hiraoka, M., Delpy, D.T.: A finite element approach for modeling photon transport in tissue. Med. Phys. 20(2), 299–309 (1993)CrossRef
11.
Scherzer: Convergence rates of iterated Tikhonov regularized solutions of nonlinear III - posed problems. Numerische Mathematik (1993)
12.
Reddi, S.J., Kale, S., Kumar, S.: On the convergence of adam and beyond. In: Conference Paper at ICLR (2018)
13.
Schweiger, M., Arridge, S.R.: The Toast++ software suite for forward and inverse modeling in optical tomography. J. Biomed. Opt. 19(4), 040801 (2014)CrossRef
Metadata
Title
Comparison Between Gradient Descent and Adam Algorithms for Image Reconstruction in Diffuse Optical Tomography
Authors
Nada Chakhim
Mohamed Louzar
Abdellah Lamnii
Mohammed Alaoui
Copyright Year
2024
Book
Applied Mathematics and Modelling in Finance, Marketing and Economics

Print ISBN: 978-3-031-42846-3

Electronic ISBN: 978-3-031-42847-0

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-42847-0_13

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