传输方程下基于模型的光学层析图像重建

Model-based Optical Tomography Reconstruction from Transport Equation

为克服光学层析图像重建的病态性,采用一种基于模型的重建方法来进行图像重建。由于广义高斯马尔可夫随机场模型具有全局平滑、边缘保留等特性,因此将其引入到服从辐射传输方程的光学层析图像重建中,并将其作为图像先验信息,同时通过最大后验概率理论,利用基于梯度的迭代优化算法来对目标函数进行优化求解。鉴于目标函数关于光学参数的梯度计算是算法中的难点,对此,提出了一种基于梯度树的梯度计算方法。实验证明:该方法与不带有先验模型的重建方法相比,不仅可进一步提高图像的重建质量,而且可降低重建病态性。

The model-based reconstruction algorithm is adopted in order to conquer the ill-posedness in optical tomography. An edge-preserving, global smoothing generalized Gaussian Markov random field（GGMRF） is imported into optical tomography reconstruction based on the radiative transfer equation in this paper. The iteration optimization method is used to solve the objective function with the GGMRF model by maximizing the a posterior probability, but the gradient computation of the objective function with respect to optical parameters is difficult. Therefore, a novel gradient computation strategy based on gradient tree is proposed. Experimental results show that this kind of reconstruction technology can improve the image reconstruction quality and decrease the ill-posedness compared to the reconstruction algorithm without priori model.