Automatic differentiation as an effective tool in Electrical Impedance Tomography

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.