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

Abstract

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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> regularization (0 <; p <; 2) is effective for overcoming these disadvantages, and efforts have been made to use regularization from the most popular L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> to its variants L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> and L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sub> . Nevertheless, L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> 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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> 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.