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An efficient Quasi-Newton method for nonlinear inverse problems via learned singular values

Smyl, D; Tallman, T; Liu, D; Hauptmann, A; (2021) An efficient Quasi-Newton method for nonlinear inverse problems via learned singular values. IEEE Signal Processing Letters 10.1109/LSP.2021.3063622. (In press). Green open access

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Abstract

IEEE Solving complex optimization problems in engineering and the physical sciences requires repetitive computation of multi-dimensional function derivatives, which commonly require computationally-demanding numerical differentiation such as perturbation techniques. In particular, Gauss-Newton methods are used for nonlinear inverse problems that require iterative updates to be computed from the Jacobian and allow for flexible incorporation of prior knowledge. Computationally more efficient alternatives are Quasi-Newton methods, where the repeated computation of the Jacobian is replaced by an approximate update, but unfortunately are often too restrictive for highly ill-posed problems. To overcome this limitation, we present a highly efficient data-driven Quasi-Newton method applicable to nonlinear inverse problems, by using the singular value decomposition and learning a mapping from model outputs to the singular values to compute the updated Jacobian. Enabling time-critical applications and allowing for flexible incorporation of prior knowledge necessary to solve ill-posed problems. We present results for the highly non-linear inverse problem of electrical impedance tomography with experimental data.

Type: Article
Title: An efficient Quasi-Newton method for nonlinear inverse problems via learned singular values
Open access status: An open access version is available from UCL Discovery
DOI: 10.1109/LSP.2021.3063622
Publisher version: http://dx.doi.org/10.1109/LSP.2021.3063622
Language: English
Additional information: This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/10125434
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