A fully non-linear optimization approach to acousto-electric tomography. (17th August 2018)

• Record Type: Journal Article
• Authors: Adesokan, B J; Knudsen, K; Krishnan, V P; Roy, S
• Is Part Of: Inverse problems. Volume 34:Number 10(2018:Oct.)
• Publication Date: 2018-08-17
• Subjects: acousto-electric tomography -- non-linear PDE optimization -- hybrid imaging -- non-linear conjugate gradient; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aad6b1
• Languages: English
• ISSNs: 0266-5611

Abstract

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.