  The aim of Electrical Impedance Tomography (EIT) is to determine the
electrical conductivity distribution inside a domain by applying currents and
measuring voltages on its boundary. Mathematically, the EIT reconstruction task
can be formulated as a non-linear inverse problem. The Bayesian inverse
problems framework has been applied expensively to solutions of the EIT inverse
problem, in particular in the cases when the unknown conductivity is believed
to be blocky. Recently, the Sparsity Promoting Iterative Alternating Sequential
(PS-IAS) algorithm, originally proposed for the solution of linear inverse
problems, has been adapted for the non linear case of EIT reconstruction in a
computationally efficient manner. Here we introduce a hybrid version of the
SP-IAS algorithms for the nonlinear EIT inverse problem, providing a detailed
description of the implementation details, with a specific focus on parameters
selection. The method is applied to the 2023 Kuopio Tomography Challenge
dataset, with a comprehensive report of the running times for the different
cases and parameter selections.
