Studies of an Adaptive Kaczmarz Method for Electrical Impedance Imaging

We present an adaptive Kaczmarz method for solving the inverse problem in electrical impedance tomography and determining the conductivity distribution inside an object from electrical measurements made on the surface. To best characterize an unknown conductivity distribution and avoid inverting the Jacobian-related term JTJ which could be expensive in terms of memory storage in large scale problems, we propose to solve the inverse problem by adaptively updating both the optimal current pattern with improved distinguishability and the conductivity estimate at each iteration. With a novel subset scheme, the memory-efficient reconstruction algorithm which appropriately combines the optimal current pattern generation and the Kaczmarz method can produce accurate and stable solutions adaptively compared to traditional Kaczmarz and Gauss-Newton type methods. Several reconstruction image metrics are used to quantitatively evaluate the performance of the simulation results.