Abstract
Medical imaging modalities are vast and include the well-established techniques of Computerized Tomography (CT), Magnetic Resonance Imaging (MRI) or Ultrasounds. Though the underlying physics differs amongst modalities, a similar Inverse Mapping is shared: the recovery of the internal physical property under analysis from measurements obtained at the exterior of the body. In the lesser common technique of Electrical Impedance Tomography (EIT), measurement of the voltage levels around a body part are used to retrieve the internal distribution map for conductivity. The complexity of the Inverse Problem in EIT surpasses that found for the Forward Problem (or Mapping), both in terms of mathematical formulation and computational overload. The ill-posed nature of the Inverse Problem further contributes to that intricacy, and solutions to tackle it will be presented in this paper by means of a non-linear optimization scheme involving the iterative Gauss-Newton (GN) method with Total Variation (TV) regularization, applied to two-dimensional (2D) body domains only. The proposed scheme is also compared to other traditional reconstruction algorithms like 2D back-projection and the sensitivity approximation to the Jacobian matrix of the system of equations governing EIT. Results from conductivity map reconstructions in anatomical phantoms have shown an improvement in signal-to-noise ratio (SNR) and distribution map error (DME) of 36% and 11% for the proposed non-linear method relative to the back-projection and single-step GN method with sensitivity approximation.
Multi-objective evolutionary framework for non-linear system identification: A comprehensive investigation