Lagrangian-based methods for finding MAP solutions for MRF models
Lagrangian-based methods for finding MAP solutions for MRF models
复制标题
基于拉格朗日的方法寻找 MRF 模型的 MAP 解
DOI：
10.1109/83.826783
复制
发表时间：
2000
期刊：
影响因子：
--
通讯作者：
G. Dahl
中科院分区：
文献类型：
--
作者：
G. Storvik;G. Dahl
基于先验马尔可夫随机场（MRF）模型从噪声图像中寻找最大后验概率（MAP）解是一项巨大的计算任务。在本文中，我们将计算问题转化为一个整数线性规划（ILP）问题。我们探讨了使用拉格朗日松弛（LR）的方法来解决MAP问题。特别是，三个不同的算法的基础上LR。所有的方法是竞争力的替代常用的基于模拟的算法的基础上马尔可夫链蒙特卡罗技术。在已经测试的所有示例（包括模拟和真实的图像）中，最好的方法基本上在少量迭代中找到MAP解决方案。此外，LR方法提供了下和上界的后验，这使得它能够评估解决方案的质量，并构造一个停止准则的算法。虽然已经应用了加性高斯噪声模型，但任何加性噪声模型都适合该框架。
Finding maximum a posteriori (MAP) solutions from noisy images based on a prior Markov random field (MRF) model is a huge computational task. In this paper, we transform the computational problem into an integer linear programming (ILP) problem. We explore the use of Lagrange relaxation (LR) methods for solving the MAP problem. In particular, three different algorithms based on LR are presented. All the methods are competitive alternatives to the commonly used simulation-based algorithms based on Markov Chain Monte Carlo techniques. In all the examples (including both simulated and real images) that have been tested, the best method essentially finds a MAP solution in a small number of iterations. In addition, LR methods provide lower and upper bounds for the posterior, which makes it possible to evaluate the quality of solutions and to construct a stopping criterion for the algorithm. Although additive Gaussian noise models have been applied, any additive noise model fits into the framework.