Electrical Impedance Tomography reconstruction using ℓ1 norms for data and image terms

Electrical Impedance Tomography (EIT) calculates the internal conductivity distribution within a body from current simulation and voltage measurements on the body surface. Two main technical difficulties of EIT are its low spatial resolution and sensitivity to measurement errors. Image reconstruction using ℓ1 norms allows addressing both difficulties, in comparison to traditional reconstruction using ℓ2 norms. A ℓ1 norm on the data residue term reduces the sensitivity to measurement errors, while the ℓ1 norm on the image prior reduces edge blurring. This paper proposes and tests a general lagged diffusivity type iterative method for EIT reconstructions ℓ1 and ℓ2 minimizations can be flexibly chosen on the data residue and/or image prior parts. Results show the flexibility of the algorithm and the merits of the ℓ1 solution.