Automatic differentiation as an effective tool in Electrical Impedance Tomography

TL;DR

This paper explores the use of automatic differentiation to efficiently solve inverse problems in Electrical Impedance Tomography, demonstrating its advantages over traditional derivative computation methods in accuracy and scalability.

Contribution

It introduces the application of automatic differentiation to EIT inverse problems and evaluates its effectiveness and scalability compared to manual derivative methods.

Findings

AD provides more accurate solutions than manual derivatives.

AD reduces development complexity for inverse solvers.

Scalability of AD depends on infrastructure and model resolution.

Abstract

Determining physical properties inside an object without access to direct measurements of target regions can be formulated as a specific type of \textit{inverse problem}. One of such problems is applied in \textit{Electrical Impedance Tomography} (EIT). In general, EIT can be posed as a minimization problem and solved by iterative methods, which require knowledge of derivatives of the objective function. In practice, this can be challenging because analytical closed-form solutions for them are hard to derive and implement efficiently. In this paper, we study the effectiveness of \textit{automatic differentiation (AD)} to solve EIT in a minimization framework. We devise a case study where we compare solutions of the inverse problem obtained with AD methods and with the manually-derived formulation of the derivative against the true solution. Furthermore, we study the viability of AD for large scale inverse problems by checking the memory and load requirements of AD as the resolution of the model increases. With powerful infrastructure, AD can pave the way for faster and simpler inverse solvers and provide better results than classical methods.