二维经验模式分解若干问题及在图像处理中应用

Bi-dimensional empirical mode decomposition (BEMD), a technique available for two-dimensional cases extended from the method of empirical mode decomposition called as Huang transform, provides a new approach to meet the requirement of analyzing non-stationary signal features in image processing, due to its good data-driven adaptive ability. However, applications have found that there are some problems associated with its interpolation optimization, end effects, stopping criteria and mode mixing. In this project, we will build an efficient bi-dimensional empirical mode decomposition algorithm based on the empirical model decomposition. The main contents include: (1) An interpolation technique based on the particle swarm optimization and the fractal description is proposed, in which the fractal Brownian function method is introduced to obtain the feature quantities of an image, and then the interpolation is operated;(2) An approach to end effect treatment is presented by means of the combination of the adaptive support vector extension with the mirror closure technique. The proposed approach weakens or even eliminates end effects of the BEMD;(3) A stopping criterion is established on the basis of the number of extreme points and its variation rate when the sieve surfaces give the projection of extreme points at different locations on the zero-mean-value plane, and the phenomena of over and under decomposition are effectively eliminated;(4) The adaptive noise-aided data analysis derives a method to suppress the mode mixing in the BEMD.The case study shows that the proposed method can satisfactorily remove the mode mixing generated in the decomposition process;(5) Research on the application of bi-dimensional empirical mode decomposition theory in image denoising, feature extraction and fusion, and put forward the solution to these problems and verify it through experiments.A large number of implementation cases illustrated in this work verify good application effects of the proposed technical measures in image processing.

二维经验模式分解是黄变换经验模式分解方法的二维拓展，它具有良好的自适应性能力，为满足图像处理中非平稳信号特征分析的需要提供了新的技术措施。然而，它存在插值优化、端部效应、停止条件、模式混叠等问题。本项目中，着手建立高效二维经验模式分解算法，包括：.(1) 提出了基于粒子群分形的插值技术，提高二维经验模式分解的插值精度和效率；(2) 提出了一种基于自适应支持向量机延拓和镜像闭合技术相结合的端部效应处理方法，抑制二维经验模式分解过程中的端部效应；(3) 建立了基于筛分曲面在零值平面上投影位置不重合极值点数目及其变化速度的停止条件，有效消除图像的过度分解和欠分解现象；(4) 提出了基于自适应噪声辅助数据分析的二维经验模式分解模式混叠消除方法，消除分解过程中产生的模式混叠；(5) 研究二维经验模式分解理论在图像处理中应用问题，提出相应解决方法。大量图像处理实例证实了所提出技术方法良好的应用效果。

二维经验模式分解是黄变换经验模式分解方法的二维拓展，它具有良好的自适应性能力，为满足图像处理中非平稳信号特征分析的需要提供了新的技术措施。然而，它存在插值优化、端部效应、停止条件、模式混叠等问题。因此，本项目针对影响二维经验模式分解算法性能的插值优化、端部效应、停止条件及模式混叠等问题展开研究，分别提出了基于粒子群分形的插值技术、基于自适应支持向量机延拓和镜像闭合技术相结合的端部效应处理方法、基于筛分曲面在零值平面上投影位置不重合极值点数目及其变化速度的停止条件和基于自适应噪声辅助数据分析的二维经验模式分解模式混叠消除方法。相关实证研究表明本项目较好地解决了二维经验模式分解算法存在的插值优化、端部效应、停止条件以及模式混叠等问题，为二维经验模式分解算法的研究和发展提供具有价值的研究成果和结论。