Automatic selection of regularization parameters for dynamic fluorescence molecular tomography: a comparison of L-curve and U-curve methods.

Maomao Chen,Chuangjian Cai,Dong Zhang,Jianwen Luo,Han Su,Yuan Zhou

doi:10.1364/boe.7.005021

Abstract

Dynamic fluorescence molecular tomography (FMT) is a promising technique for the study of the metabolic process of fluorescent agents in the biological body in vivo, and the quality of the parametric images relies heavily on the accuracy of the reconstructed FMT images. In typical dynamic FMT implementations, the imaged object is continuously monitored for more than 50 minutes. During each minute, a set of the fluorescent measurements is acquired and the corresponding FMT image is reconstructed. It is difficult to manually set the regularization parameter in the reconstruction of each FMT image. In this paper, the parametric images obtained with the L-curve and U-curve methods are quantitatively evaluated through numerical simulations, phantom experiments and in vivo experiments. The results illustrate that the U-curve method obtains better accuracy, stronger robustness and higher noise-resistance in parametric imaging. Therefore, it is a promising approach to automatic selection of the regularization parameters for dynamic FMT.

Highlights

Fluorescence molecular tomography (FMT) is an emerging imaging technique that allows for noninvasive and quantitative reconstruction of three-dimensional (3D) distribution of fluorescent agents in the biological body in vivo [1]
For dynamic FMT (DFMT) problems, the small animal is fixed on the stage and continuously rotated for K minutes to monitor the metabolic process of the fluorescent agents
The mean parameter of the L-curve method increases from 1.15 × to 2.44 × when the signal-to-noise ratios (SNRs) drops from 40 dB to 20 dB, while the mean parameters of the U-curve method are very stable for all the noise levels

Summary

Introduction

Fluorescence molecular tomography (FMT) is an emerging imaging technique that allows for noninvasive and quantitative reconstruction of three-dimensional (3D) distribution of fluorescent agents in the biological body in vivo [1]. By adding time as a new dimension, dynamic FMT (DFMT) can be used for pharmacokinetic studies [2, 3], which reflect the absorption, distribution and excretion characteristics of fluorescent agents inside the biological tissues. In order to monitor the metabolic process of fluorescent agents in the body, the imaged object is continuously monitored for tens of minutes. In order to obtain a meaningful solution, the FMT reconstruction problem must be regularized, for example, using Tikhonov regularization, and a regularization parameter λ is required. In a typical DMFT implementation, the imaged object is monitored for more than 50 minutes, and the fluorescent concentration varies with time. Each set of the fluorescent measurements should be considered as an independent FMT reconstruction problem, in which a particular regularization parameter should be used. Tens of different regularization parameters are required and are very difficult to choose manually

Methods

Results

Conclusion