Matrix-Free Gauss-Newton Method for Large-Scale Electrical Impedance Tomography

Electrical impedance tomography (EIT) is a non-invasive imaging technique that reconstructs the internal conductivity distribution of a target object, with applications spanning medical imaging, geophysics, and industrial process monitoring. While the iterative Gauss-Newton (GN) method is widely adopted for its superior reconstruction accuracy, conventional implementations suffer from prohibitive computational and memory demands in large-scale EIT problems. To overcome these limitations, this study introduces the concept of a single electrode model (SEM), which streamlines the calculation of the Jacobian matrix. Building upon SEM, we propose a computationally efficient implementation of the matrix-free Gauss-Newton (MF-GN) method for EIT, which eliminates the need for explicit storage and manipulation of large Jacobian matrices. The proposed MF-GN method attains reconstruction accuracy comparable to that of the conventional GN method while reducing memory usage by orders of magnitude and substantially accelerating computation for large-scale systems. Numerical experiments and real-data validations demonstrate its efficacy, underscoring the potential of MF-GN for solving large-scale EIT problems.