High-Resolution Reconstruction of FMT Based on Elastic Net Optimized by Relaxed ADMM

Fluorescence Molecular Tomography (FMT), providing thethree-dimensional fluorescent distribution information of specific molecular probes in tumors, is widely applied to detect
in vivo
tumors. However, the ill-posedness of reconstruction greatly affects the resolution of FMT. Traditional methods have introduced different regularization terms to solve this problem, but there are still challenges for the high-resolution reconstruction of small tumors under complex conditions. In this paper, we proposed an elastic net method optimized by the relaxed Alternating Direction Method of Multipliers (EN-RADMM) to improve the reconstruction resolution for small tumors. The objective function consisted of the Least-Square term and elastic net regularization. Relaxation, equivalent deformation directing at ill-posed equations, and LU decomposition were applied to accelerate algorithm convergence and improve solution accuracy. Thereby, the light from small tumors can be precisely reconstructed. We designed a series of digital tumor models with different distances, sizes, and shapes to verify the performance of EN-RADMM, and utilized the real glioma-bearing mouse models to further verify its feasibility and accuracy. The simulation results demonstrated that EN-RADMM can achieve significantly higher resolution and reconstruction accuracy of morphology and position with less time compared with other advanced methods. Furthermore,
in vivo
experiments proved the broad prospect of EN-RADMM in pre-clinical application of FMT reconstruction.