A Sparsity-Constrained Preconditioned Kaczmarz Reconstruction Method for Fluorescence Molecular Tomography

Adaptive permissible region based random Kaczmarz reconstruction method for localization of carotid atherosclerotic plaques in fluorescence molecular tomography

Objective. In this study, we propose the adaptive permissible region based random Kaczmarz method as an improved reconstruction method to recover small carotid atherosclerotic plaque targets in rodents with high resolution in fluorescence molecular tomography (FMT). Approach. We introduce the random Kaczmarz method as an advanced minimization method to solve the FMT inverse problem. To satisfy the special condition of this method, we proposed an adaptive permissible region strategy based on traditional permissible region methods to flexibly compress the dimension of the solution space. Main results. Monte Carlo simulations, phantom experiments, and in vivo experiments demonstrate that the proposed method can recover the small carotid atherosclerotic plaque targets with high resolution and accuracy, and can achieve lower root mean squared error and distance error (DE) than other traditional methods. For targets with 1.5 mm diameter and 0.5 mm separation, the DE indicators can be improved by up to 40%. Moreover, the proposed method can be utilized for in vivo locating atherosclerotic plaques with high accuracy and robustness. Significance. We applied the random Kaczmarz method to solve the inverse problem in FMT and improve the reconstruction result via this advanced minimization method. We verified that the FMT technology has a great potential to locate and quantify atherosclerotic plaques with higher accuracy, and can be expanded to more preclinical research.