基于高阶马尔科夫随机场的图像去噪声研究

在图像去噪声处理中，高阶马尔科夫随机场通过最小化能量函数达到最优的去噪声结果。为了提高能量函数的优化性能，本文在马尔科夫随机场子模性的基础上对原始问题和对偶问题进行了分析，提出了一种基于原始-对偶方法的子模块之和方法。首先，描述了马尔科夫随机场的线性规划及其对偶问题，并介绍了子模块之和流方法。接下来，通过对子模块之和流方法的原始问题和对偶问题进行分析，提出了同时满足派系松弛和一元松弛条件的近似解计算方法。实验表明，本文提出的方法与四种典型的图像去噪声方法相比具有更好的效果和更短的运行时间。

Research of Image Denoising Based on High-Order Markov Random Fields

In image denoising, higher-order Markov random fields achieve the best result of image denoising by minimizing its energy function. In order to optimize the performance of energy function, this paper analyzes the primal and dual problem of Markov random fields based on submodularity, and proposes a primal-dual based sum-of-submodular flow approach. Firstly, we describe the linear programming and its dual problem of Markov random fields, and introduce the sum-of-submodular flow method. Next, according to analyzing the primal and dual problem of the sum-of-submodular flow method, we propose an approximating method satisfying both unary and clique slackness conditions. The experiments show that, the proposed approach is more efficient and has less executing time than four classical methods in image denoising.