A robust elastic net-ℓ 1 ℓ 2 reconstruction method for x-ray luminescence computed tomography

Abstract

Objective. X-ray luminescence computed tomography (XLCT) has played a crucial role in pre-clinical research and effective diagnosis of disease. However, due to the ill-posed of the XLCT inverse problem, the generalization of reconstruction methods and the selection of appropriate regularization parameters are still challenging in practical applications. In this research, an robust Elastic net-ℓ1ℓ2 reconstruction method is proposed aiming to the challenge. Approach. Firstly, our approach consists of ℓ1 and ℓ2 regularization to enhance the sparsity and suppress the smoothness. Secondly, through optimal approximation of the optimization problem, double modification of Landweber algorithm is adopted to solve the Elastic net-ℓ1ℓ2 regulazation. Thirdly, drawing on the ideal of supervised learning, multi-parameter K-fold cross validation strategy is proposed to determin the optimal parameters adaptively. Main results. To evaluate the performance of the Elastic net-ℓ1ℓ2 method, numerical simulations, phantom and in vivo experiments were conducted. In these experiments, the Elastic net-ℓ1ℓ2 method achieved the minimum reconstruction error (with smallest location error, fluorescent yield relative error, normalized root-mean-square error) and the best image reconstruction quality (with largest contrast-to-noise ratio and Dice similarity) among all methods. The results demonstrated that Elastic net-ℓ1ℓ2 can obtain superior reconstruction performance in terms of location accuracy, dual source resolution, robustness and in vivo practicability. Significance. It is believed that this study will further benefit preclinical applications with a view to provide a more reliable reference for the later researches on XLCT.