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

Owing to its low cost, fast response, non-invasiveness, 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 <inline-formula> <tex-math notation="LaTeX">$L_{p}$ </tex-math></inline-formula> regularization (<inline-formula> <tex-math notation="LaTeX">$0 < \textit {p} < 2$ </tex-math></inline-formula>) is effective for overcoming these disadvantages, and efforts have been made to use regularization from the most popular <inline-formula> <tex-math notation="LaTeX">$L_{2}$ </tex-math></inline-formula> to its variants <inline-formula> <tex-math notation="LaTeX">$L_{1}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$ L_{1/2}$ </tex-math></inline-formula>. Nevertheless, <inline-formula> <tex-math notation="LaTeX">$L_{p}$ </tex-math></inline-formula> regularization is generally difficult to be solved fast and efficiently, and the selection of <italic>p</italic> 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 <inline-formula> <tex-math notation="LaTeX">$L_{p}$ </tex-math></inline-formula> regularization for EIT, with <italic>p</italic> 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.

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