Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China.
IEEE Trans Image Process. 2009 Dec;18(12):2797-802. doi: 10.1109/TIP.2009.2028369. Epub 2009 Jul 24.
In this paper, we construct a Lattice Boltzmann scheme to simulate the well known total variation based restoration model, that is, ROF model. The advantages of the Lattice Boltzmann method include the fast computational speed and the easily implemented fully parallel algorithm. A conservative property of the LB method is discussed. The macroscopic PDE associated with the LB algorithm is derived which is just the ROF model. Moreover, the linearized stability of the method is analyzed. The numerical computations demonstrate that the LB algorithm is efficient and robust. Even though the quality of the restored images is slightly lower than those by using the ROF model, the restored images of the LB method are satisfactory. Furthermore, computational speed of the LB method is much faster than ROF model. In general, CPU time of the LB method for restored images is about one tenth of ROF model.
在本文中，我们构建了一个格子玻尔兹曼方案来模拟著名的全变分重建模型，即 ROF 模型。格子玻尔兹曼方法的优点包括计算速度快和易于实现的完全并行算法。讨论了 LB 方法的保守性质。推导出与 LB 算法相关的宏观 PDE，它恰好是 ROF 模型。此外，还分析了方法的线性稳定性。数值计算表明，LB 算法是高效和稳健的。尽管重建图像的质量略低于使用 ROF 模型的质量，但 LB 方法的重建图像令人满意。此外，LB 方法的计算速度比 ROF 模型快得多。一般来说，LB 方法用于恢复图像的 CPU 时间约为 ROF 模型的十分之一。
