【作者】 葛光涛；

【导师】 桑恩方；

【作者基本信息】 哈尔滨工程大学 ， 信号与信息处理， 2009， 博士

【摘要】 二维经验模态分解是将Hilbert-Huang变换向二维信号处理上的一种推广,有可能成为一种全新的二维信号处理方法。二维经验模态分解是一个开放性的问题,其算法本身尚有许多需要完善的地方；而二维经验模态分解的应用研究也是目前图像处理领域里的一个研究热点。本文首先研究了二维经验模态分解算法的优化问题,在现有几种比较成功的曲面拟合算法的基础上分析了获得正确模态所需要的合理的筛分次数问题,并提出了基于被筛分曲面极值点数量和分布变化规律的筛分停止准则。本文将模态分解中取上下包络均值的过程定义为包络均值运算,进而推导出各个模态的包络均值表示式,分解出了二维模态分解过度筛分之后得到的各个模态图像中异常信息的成分,并分析了这些成分和对应模态之间的跟随关系。根据BEMD的空间滤波特性和过筛分成分与对应模态之间的跟随关系,提出了二维空间域限带信号的包络均值运算的简单数学模型假设,并据此假设对BEMD无穷多次筛分的结果作了猜想。其后,本文对新准则下获得模态的各方面性质进行了分析。对二维模态的分析主要涉及的几个方面包括：能量,频率,相位和可分离度等等。这样的分析一方面证明了新准则的合理性,另一方面也丰富了二维信号的相位理论,为后续的应用研究提供了理论支持。在二维经验模态分解的应用研究中,本文根据二维信号的相位理论改进了几种传统的纹理分割方法,并且分析了将二维经验模态分解理论引入到纹理分割中的可能性和应用价值,基于不同纹理分析方法对不同类型纹理具有不同捕捉能力的特点提出了并行叠加的无监督聚类思想；而根据文中前半部分提出的包络均值表示式和对各模态的性质分析,将利用网格特征点表示出来的各个均值曲面分别进行压缩,再根据余量的包络均值表示式将各个均值曲面分别重建后再相加就得到了第一余量曲面(图像)的高质量的还原结果。将余量曲面的压缩结果与Linderhed的VSDCTEMD方法结合,就得到了改进的基于二维经验模态分解的图像压缩方法。本文提出的算法分别在光学图像和侧扫声纳图像的处理中经过大量的实验,实验证明了文中算法的正确性和可靠性。更多还原

【Abstract】 The Bidimensional Empirical mode decomposition (BEMD) theory is the extention of the Hilbert-Huang transform to the two-dimensional signal processing, and it would be another successful two-dimensional signal processing approach. The BEMD is an open research, whose primary algorithm is to be perfected, and its application research is also a hotspot in the field of image processing.This dissertation studies on optimizing the BEMD algorithm firstly. On the basis of several effective surface-fitting algorithms, the reasonable sifting times is analyzed to get the right Intrinsic Mode Function (IMF), and the criterion for stopping the sifting process based on the characteristic points changing rule is brought out. The Empirical mode decomposition course of getting mean envelope is definited as mean envelope operation, so as to deduce the formula to express the IMFs with mean envelopes, the abnormal components existing in the over-sifting IMFs are extracted out, and the follow relationship between these components and their corresponding IMFs is analyzed. According to this follow relationship and the filter bank feature of the BEMD, the hypothesis about the mean envelope operation on the two-dimensional space frequency band limited signal is advised, and according to this hypothesis, the guess about the result of the BEMD infinite sifting is brought out.For the next step, the IMF’s qualities under the new criterion is analyzed, mainly including the energy, the frequency, the phase and the detachable degree, to prove the reasonability of the new criterion on one hand, and to enrich the two-dimensional signal phase theory on the other hand, which will support the application research latterly.In applications, several classic texture segmentation approaches are modified according to the two-dimensional phase theory, and the possibility and the applied values of taking BEMD into the texture segmentation issue are analyzed. Considering the different effects of the different texture distinguishing instruments, the idea of the side-by-side overlapping unsupervised classification is brought out. According to the mean envelope operation and the quality of the IMF, the several mean surfaces are respectively compressed by representing them with the grid characteristic points, and the high quality reconstruction of the first residue surface (image) is got by adding the several reconstructed mean surfaces together. Combined residue compression with Linderhed’s VSDCTEMD approach, the improved image compression approach is achieved.Several ways to examine the algorithms on the optical or the underwater acoustic images are performed; and the result proves the rightness and reliability of the method in this dissertation.更多还原