Mixed Total Variation and L(1) Regularization Method for Optical Tomography Based on Radiative Transfer Equation.
Mixed Total Variation and L(1) Regularization Method for Optical Tomography Based on Radiative Transfer Equation.
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DOI：
10.1155/2017/2953560
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发表时间：
2017
影响因子：
--
通讯作者：
Li L
中科院分区：
文献类型：
--
作者：
Tang J;Han B;Han W;Bi B;Li L
光学层析成像是一种新兴的和重要的分子成像方式。光学层析成像的目的是重建人体组织的光学特性。本文主要研究基于辐射传输方程（RTE）的吸收系数重建问题。这是一个不适定的参数识别问题。正则化方法已被广泛应用于光学系数的重建，如全变分（TV）正则化和L1正则化。为了更好地重建分段常数和稀疏系数分布，TV和L1范数结合作为正则化。正问题在空间上采用间断伽辽金法离散，在角空间上采用有限元法离散。最小化问题的解决雅可比的Levenberg-Marquardt型方法，配备了分裂Bregman算法的L1正则化。我们使用伴随方法来计算雅可比矩阵，大大提高了计算效率。通过与其他基于TV和L1正则化的图像重建方法的比较，仿真结果表明了该方法的有效性和有效性。
Optical tomography is an emerging and important molecular imaging modality. The aim of optical tomography is to reconstruct optical properties of human tissues. In this paper, we focus on reconstructing the absorption coefficient based on the radiative transfer equation (RTE). It is an ill-posed parameter identification problem. Regularization methods have been broadly applied to reconstruct the optical coefficients, such as the total variation (TV) regularization and the L1 regularization. In order to better reconstruct the piecewise constant and sparse coefficient distributions, TV and L1 norms are combined as the regularization. The forward problem is discretized with the discontinuous Galerkin method on the spatial space and the finite element method on the angular space. The minimization problem is solved by a Jacobian-based Levenberg-Marquardt type method which is equipped with a split Bregman algorithms for the L1 regularization. We use the adjoint method to compute the Jacobian matrix which dramatically improves the computation efficiency. By comparing with the other imaging reconstruction methods based on TV and L1 regularizations, the simulation results show the validity and efficiency of the proposed method.