Abstract: For the three-dimensional（3-D） reconstruction of the fluorescence microscopic image, this paper adopts the total generalized variation and shearlet transform as regularization term to construct image reconstruction model. Aiming at the high order and non-smooth feature of the reconstruction model, the proposed model is solved via the Variable Splitting（VS） theory and the Split Bregman（SB） method. In this paper an image 3-D reconstruction method is proposed to achieve edge preservation and to avoid oil-painting artifacts for fluorescence microscopic samples. By appropriately choosing the reasonable parameters, the best restoration result can be obtained. The experimental results show the effectiveness and feasibility of the proposed algorithm in terms of the synthetic image stack and real fluorescence microscopic image stack.

Key words: three-dimensional reconstruction, total generalized variation, shearlet transform, variable splitting, split Bregman

摘要： 针对荧光显微图像三维重建问题，采用广义全变差和剪切波变换作为重建图像的正则项，并构建重建模型，针对重建模型的高阶与非光滑特性，提出了基于变量分离理论和分裂Bregman迭代的快速重建算法，该算法不仅能够实现边缘保存，避免阶梯效应，还可以通过合理选择参数，获得很好的重建效果，在模拟图像栈和真实荧光显微图像栈的实验结果验证了该算法的有效性和可行性。

关键词: 三维重建, 广义全变差, 剪切波变换, 变量分离, 分裂Bregman