University of Oulu

D. Smyl, T. Tallman, D. Liu and A. Hauptmann, "An efficient Quasi-Newton method for nonlinear inverse problems via learned singular values," in IEEE Signal Processing Letters, doi: 10.1109/LSP.2021.3063622

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

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Author: Smyl, Danny1; Tallman, Tyler N.2; Liu, Dong3;
Organizations: 1Department of Civil and Structural Engineering, University of Sheffield, UK
2School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN, USA
3CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei, 230026, China
4Research Unit of Mathematical Sciences; University of Oulu, Oulu, Finland
5Department of Computer Science; University College London, London, United Kingdom
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 4.7 MB)
Persistent link:
Language: English
Published: Institute of Electrical and Electronics Engineers, 2021
Publish Date: 2021-03-22


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.

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Series: IEEE signal processing letters
ISSN: 1070-9908
ISSN-E: 1558-2361
ISSN-L: 1070-9908
Volume: Early Access
DOI: 10.1109/LSP.2021.3063622
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
113 Computer and information sciences
114 Physical sciences
212 Civil and construction engineering
Funding: This work was supported by Academy of Finland Proj. 336796, 334817, and the CMIC-EPSRC platform grant (EP/M020533/1), DL was supported by National Natural Science Foundation of China (Grant No. 61871356).
Academy of Finland Grant Number: 336796
Detailed Information: 336796 (Academy of Finland Funding decision)
334817 (Academy of Finland Funding decision)
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