Adaptive $L_{p}$ Regularization for Electrical Impedance Tomography

Owing to its low cost, fast response, noninvasiveness, and non-radiation, electrical impedance tomography (EIT) has been applied to numerous fields. However, its spatial resolution is low due to the inherent ill-posed problem and the “soft field” effect. The L
_p
regularization (0 <; p <; 2) is effective for overcoming these disadvantages, and efforts have been made to use regularization from the most popular L
₂
to its variants L
₁
and L
_1/2
. Nevertheless, L
_p
regularization is generally difficult to be solved fast and efficiently, and the selection of p yielding the best result is also a problem. In this paper, an adaptive re-weighted (ARW) algorithm with a general frame is presented to solve the L
_p
regularization for EIT, with p for each pixel determined adaptively in iterations. Experiments were carried out to validate the proposed algorithm. Results show that compared with other EIT algorithms, the ARW algorithm had a higher spatial resolution. Moreover, it can provide a wider range of selection for regularization parameter, which increases the practicality of the proposed algorithm.