Robust reconstruction of fluorescence molecular tomography by minimizing the capped L2,p norm

Abstract

Fluorescence molecular tomography (FMT) is a promising imaging modality capable of reconstructing the three-dimensional spatial distribution of interior fluorescent targets. Several compressed sensing (CS)-based methods have been proposed for reconstruction. However, these methods perform poorly in the presence of noise, as they typically employ the squared $L_2$ norm to measure reconstruction errors, which amplifies the negative impact of noise and compromises robustness. To address this issue, we propose a robust reconstruction model based on the capped $L_{2,p}$ norm metric, which retains the advantages of CS while enhancing robustness against noise. The capped $L_{2,p}$ norm extends traditional metrics by introducing the parameter $p$ and a capping threshold, effectively limiting the influence of large errors. Moreover, it provides greater robustness than conventional $L_2$ and $L_1$ norms by adaptively truncating extreme values. As a result, the proposed model effectively suppresses noise and outliers, leading to improved reconstruction stability. The established reconstruction model is nonsmooth and nonconvex due to the capped $L_{2,p}$ norm. To optimize it efficiently, we introduce an iterative re-weighted algorithm, termed CIRWA. Additionally, the convergence of the algorithm is theoretically analyzed. Numerical simulations and in vivo experiments are conducted to validate the performance of CIRWA. The results demonstrate that, compared with state-of-the-art methods, CIRWA achieves more accurate fluorescent target reconstruction and exhibits superior robustness. These findings suggest that CIRWA has significant potential to advance the preclinical applications of FMT.