【作者】 周欣；

【导师】 周建中； 李衷怡；

【作者基本信息】 华中科技大学 ， 系统分析与集成， 2007， 硕士

【摘要】 经验模式分解(EMD)方法是1998年Huang提出的一种新的信号处理方法,在非平稳信号分析方面有良好的性能。该方法能将复杂的非平稳信号分解成若干具有不同特征尺度的平稳的数据分量与趋势项的叠加,具有自适应性,适于处理非平稳信息。鉴于EMD方法在一维信号处理方面获得的巨大成功,国内外学者将它推广到二维,提出了二维经验模式分解(BEMD)方法,并应用于二维信号处理。由于二维信号的复杂性,一般的BEMD方法还存在许多问题有待研究。首先详细论述了一维经验模式分解和二维经验模式分解的模型和原理。然后给出了二维经验模式分解方法的实现流程。并详细介绍了筛选过程中利用数学形态学方法选取图像局部极值点,平面散乱点集delaunay三角剖分以及通过BB样条插值法求包络曲面等关键技术。另外,根据内禀模式函数的定义提出了一种新的结束条件判别方法,提高了分解速度。将二维经验模式分解(BEMD)方法应用于图像处理,可将图像分解为一系列细节信息和趋势信息。由图像的趋势信息重建图像,可达到去除图像噪声的目的。实验结果表明,与均值滤波、中值滤波和维纳滤波相比,该方法对去除乘性噪声具有较优的效果,图像峰值信噪比(PSNR)得到明显地提高。更多还原

【Abstract】 The Empirical Mode Decomposition (EMD), which has been recently introduced by Huang in 1998, is a new method of signal processing and has superior performance in non-stationary signal analysis. This method can be applied to decompose the non-stationary data into a series of data layers with different character-scale and the trend data. It is adaptive, and, therefore, suitable for processing nonlinear and non-stationary data.Because of the superior performance in one-dimensional signal processing, the EMD is extended to Bidimensional EMD (BEMD) and then applied to process bidimensional signal. On account of the complexity of bidimensional signal, the general BEMD has some shortages and need to be improved in future.In this thesis, the theories of the empirical mode decomposition (EMD) and its extension Bidimensional EMD are introduced first. Then we describe the processing flow of the BEMD. The sifting process is realized using mathematical morphology operators to detect regional extrema and thanks to delaunay triangulation and Bernstein-Bezier spline interpolation based on triangular meshes for surface interpolation. In addition, according to the definition of the intrinsic mode function, we present a new condition to end the sifting process, and it is proved that the speed of decomposition increased.By the BEMD method, an image with noise is decomposed into a series of detail data and the trend data. The noise can be removed by the image reconstruction with the trend data. Experimental results demonstrate that comparing with mean filter, median filter, wiener filter, this method has more notable performance to get rid of the multiplicative noise and the value of PSNR markedly increased.更多还原