A fully non-linear optimization approach to acousto-electric tomography

Bolaji James Adesokan, K Knudsen, V P Krishnan, S Roy*

*Corresponding author for this work

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Abstract

This paper considers the non-linear inverse problem of reconstructing an electric conductivity distribution from the interior power density in a bounded domain. Applications include the novel tomographic method known as acousto-electric tomography, in which the measurement setup in electrical impedance tomography is modulated by ultrasonic waves thus giving rise to a method potentially having both high contrast and high resolution. We formulate the inverse problem as a regularized non-linear optimization problem, show the existence of a minimizer, and derive optimality conditions. We propose a non-linear conjugate gradient scheme for finding a minimizer based on the optimality conditions. All our numerical experiments are done in two-dimensions. The experiments reveal new insight into the non-linear effects in the reconstruction. One of the interesting features we observe is that, depending on the choice of regularization, there is a trade-off between high resolution and high contrast in the reconstructed images. Our proposed non-linear optimization framework can be generalized to other hybrid imaging modalities.
Original languageEnglish
Article number104004
JournalInverse Problems
Volume34
Issue number10
Number of pages16
ISSN0266-5611
DOIs
Publication statusPublished - 2018

Keywords

  • Acousto-electric tomography
  • Non-linear PDE optimization
  • Hybrid imaging
  • Non-linear conjugate gradient

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