Discontinuous Galerkin Method for Electrical Impedance Tomography Based on Sparsity Regularization with Adam

Abstract

In this work, we develop a novel sparsity reconstruction algorithm for Electrical Impedance Tomography (EIT), focusing on problems where the region of interest contains relatively simple, localized inhomogeneities. The optimization framework employs

l^1

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-norm regularization to promote sparsity, combined with the soft shrinkage algorithm. Our key ingredient is incorporating the Adam (Adaptive Moment Estimation) algorithm for adaptive step sizes and directions, enhancing both convergence speed and accuracy. The optimization problem is solved numerically using a high-order Discontinuous Galerkin (DG) method with quadratic polynomials. Numerical results demonstrate the efficiency and accuracy of the proposed sparsity reconstruction method with Adam, with comparisons to the smoothness regularization also presented.

Keywords

Electrical impedance tomography (EIT) / Sparsity / Adam / Discontinuous Galerkin (DG) method / Partial data / 35R30 / 65J20 / 65N21

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