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

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