基于分裂Bregman方法的生物发光断层成像的全变差正则化

Total variation regularization for bioluminescence tomography with the split Bregman method.

作者信息

Feng Jinchao, Qin Chenghu, Jia Kebin, Zhu Shouping, Liu Kai, Han Dong, Yang Xin, Gao Quansheng, Tian Jie

机构信息

College of Electronic Information & Control Engineering, Beijing University of Technology, Beijing 100124, China.

出版信息

Appl Opt. 2012 Jul 1;51(19):4501-12. doi: 10.1364/AO.51.004501.

DOI:10.1364/AO.51.004501

PMID:22772124

Abstract

Regularization methods have been broadly applied to bioluminescence tomography (BLT) to obtain stable solutions, including l2 and l1 regularizations. However, l2 regularization can oversmooth reconstructed images and l1 regularization may sparsify the source distribution, which degrades image quality. In this paper, the use of total variation (TV) regularization in BLT is investigated. Since a nonnegativity constraint can lead to improved image quality, the nonnegative constraint should be considered in BLT. However, TV regularization with a nonnegativity constraint is extremely difficult to solve due to its nondifferentiability and nonlinearity. The aim of this work is to validate the split Bregman method to minimize the TV regularization problem with a nonnegativity constraint for BLT. The performance of split Bregman-resolved TV (SBRTV) based BLT reconstruction algorithm was verified with numerical and in vivo experiments. Experimental results demonstrate that the SBRTV regularization can provide better regularization quality over l2 and l1 regularizations.

摘要

正则化方法已广泛应用于生物发光断层扫描（BLT）以获得稳定解，包括l2和l1正则化。然而，l2正则化会过度平滑重建图像，而l1正则化可能会使源分布稀疏化，从而降低图像质量。本文研究了在BLT中使用总变差（TV）正则化。由于非负约束可以提高图像质量，因此在BLT中应考虑非负约束。然而，具有非负约束的TV正则化由于其不可微性和非线性而极难求解。这项工作的目的是验证分裂Bregman方法，以最小化具有非负约束的BLT的TV正则化问题。通过数值和体内实验验证了基于分裂Bregman求解的TV（SBRTV）的BLT重建算法的性能。实验结果表明，SBRTV正则化比l2和l1正则化能提供更好的正则化质量。