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

arXiv: https://arxiv.org/abs/1804.02507 · HTML: https://mlsanity.com/paper/1804.02507/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Apr 2018.

## Built on by (most cited first, 1 of 1)

- [Initial condition recovery in nonlinear damped viscous photoacoustic tomography using a convolutional neural network-guided gradient-free optimization framework](https://mlsanity.com/paper/2610.01015/) (2026)

## Abstract (arXiv)

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.