Adaptive Kaczmarz method for image reconstruction in electrical impedance tomography.

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 J(T)J which could be expensive in terms of computation cost and memory in large-scale problems, we propose solving the inverse problem by applying the optimal current patterns for distinguishing the actual conductivity from the conductivity estimate between each iteration of the block Kaczmarz algorithm. With a novel subset scheme, the memory-efficient reconstruction algorithm which appropriately combines the optimal current pattern generation with the Kaczmarz method can produce more accurate and stable solutions adaptively as compared to traditional Kaczmarz- and Gauss-Newton-type methods. Choices of initial current pattern estimates are discussed in this paper. Several reconstruction image metrics are used to quantitatively evaluate the performance of the simulation results.