Abstract: Random forest algorithm is an efficient method of single image super resolution, however its decision function is a binary function, and the definitive split on certain image blocks is not the optimal choice. For improving the performance of single image super resolution, this paper uses Gauss membership functions to build decision functions of decision nodes in random forest, which converts the output values of decision function from definitive values of 0 and 1 to probability values between 0 and 1, then predicts on leaf nodes according to the product of decision nodes’ probabilities on the route of the leaf nodes, and then learns the decision parameters in terms of minimum empirical risk metrics, to make the random forest can better learn different sample data. Experimental results show that, by comparing with random forest learning and other popular single image super resolution methods, this method can enhance the peak signal to noise ratio of super resolution images, at the same time has similar efficiency comparable with traditional random forest learning algorithm.

Key words: random forest learning, single image super resolution, decision function, Gauss membership functions, empirical risk

摘要： 随机森林学习算法是一种有效的单图像超分辨率方法，然而其决策函数是确定的二值函数，这对某些图像块的确定性划分并不是最优的选择。为提升单图像超分辨率性能，采用高斯隶属度函数构建随机森林各决策节点的决策函数，将决策函数的输出值由0和1的确定值转换到0~1之间的概率值，并在叶节点上依据数据划分路径上各决策节点概率的乘积进行预测，依据最小经验冒险准则学习决策参数，使随机森林能更好学习不同的样本数据。实验结果表明，与随机森林学习等目前主流单图像超分辨率方法相比，该方法可以提升超分辨率图像的峰值信噪比，同时运算效率与传统随机森林学习算法相当。

关键词: 随机森林学习, 单图像超分辨率, 决策函数, 高斯隶属度函数, 经验冒险