Abstract: This paper presents a novel approach to image restoration, which is based on BP neural network and High-Dimensional Space Geometric（HDSG） theory. According to principles of homeomorphisms and homology continuity in High-Dimensional Space Geometry, blurred image is mapped to a point in the high-dimensional space. The restored image is obtained through the distribution curve composed by the points which correspond to the blurred image and some offspring of this blurred image. The relationship between each point is constructed by training the PSO-BP neural network whose input and output are the three blurred images and the original clear image respectively. Then the restored images could be got from the output of the trained network by giving the blurred images to the input. Comparative experiments demonstrate that satisfying restoration results can be obtained through this approach both in visual impression and quantitative analysis.

Key words: image restoration, neural network, Particle Swarm Optimization Back Propagation（PSO-BP）, High-dimensional space geometric

摘要： 针对退化图像复原问题，提出了一种基于高维空间几何理论（HDSG）的PSO-BP神经网络图像复原方法。高维空间几何理论中的同胚映射和同源连续性原理，把图像映射为高维空间中的一个点，通过回归原模糊图像和由此图像衍生出的几幅更加模糊的图像对应在空间中几个点的分布曲线，得到清晰的复原图像。在该理论基础上，用PSO-BP神经网络来确定高维空间中各点的关系，通过对训练样本的学习训练，在三幅退化图像与原始清晰图像之间建立映射关系，然后用训练好的网络对测试样本进行复原。对比实验表明，该方法在主观视觉和定量分析上都获得了较好的效果。

关键词: 图像复原, 神经网络, 粒子群优化算法-反向传播（PSO-BP）, 高维空间几何