【作者】 乔丽红；

【导师】 蒋春澜； 彭立中；

【作者基本信息】 河北师范大学 ， 应用数学， 2010， 博士

【摘要】 图像处理作为信号处理的重要分支已成为人们研究的热点,其应用领域相当广泛,包括视频影像处理、医学图像处理、遥感图像处理等等。目前图像处理已经发展出很多分支,如图像融合、图像分割、纹理分析、图象压缩等,而图像处理的发展有待于信号处理技术的发展。信号处理领域传统的数据分析方法有傅里叶变换、Wigner-Ville分布和小波分析等,这些方法采用固定的基来分析信号,对平稳信号较有效。1998年Huang等人提出了一种新的数据分析方法–希尔伯特黄变换(Hilbert-Huang Transform简称为:HHT)方法。与传统方法完全不同,HHT方法不需要任何先验基函数,是一种针对非平稳过程的自适应时频分析方法。数据分析所需要的基函数是通过经验模式分解(Empirical ModeDecomposition,简称为:EMD)自适应的从信号中获得的,EMD分解的结果形成近似正交的内蕴模式函数(Intrinsic Mode Function,简称为:IMF)。然后,将每个IMF与其希尔伯特变换结合形成解析信号,可以求得信号的瞬时振幅和瞬时频率等重要特征,在时间–频率–振幅平面上形成希尔伯特谱。HHT方法尤其适用于分析非线性信号,被成功应用于医学、军事、海洋学等许多重要领域,具有极高的应用价值。鉴于此优点,二维HHT方法也受到人们的广泛关注。人们研究了二维EMD的分解算法,取得了一定的成果。但由于二维信号的复杂性,二维HHT方法及其应用还存在许多问题。本文对二维HHT方法的理论及其在图像处理中的应用两方面展开了研究。首先对二维EMD的分解方法及二维谱特征的提取等理论方面的问题进行了研究,改进了已有的分解方法并得到了二维瞬时频率等重要谱特征;其次我们将二维HHT理论应用于图像处理中,取得了一些的成果。具体来说,本文的主要工作如下:在理论方面,我们改进了原有的二维EMD的分解方法,并利用四元数解析提取了二维IMF的谱特征。首先,针对二维EMD算法计算时间长等问题,我们改进了BEMD方法,利用快速镜像基函数进行插值,并采用镜像对称的方法进行边界处理。这样能够加快迭代速度,抑制边界效应。我们还对二维谱特征进行了深入研究。利用四元数解析的方法得到了符合二维解析推广条件的解析信号,接着采用一种新的表示形式,提取了二维IMF的瞬时振幅、瞬时相位、两个瞬时频率、u的三个成分共七个特征。文中分别对自然图像和纹理图像进行了实验分析,实验结果表明这些特征可以较好的反映图像的内部特征,为二维HHT的发展奠定了理论基础。另一方面,我们将二维HHT方法应用到图像融合、图像解调中、分析了二维EMD的特征,并将二维瞬时频率应用到图像分离中,取得了一定的效果。下面分别进行介绍:首先,我们将二维BEMD(Bidimentional Empirical Mode Decomposition)和亮度-色度-饱和度(Intensity-Hue-Saturation,简称为:IHS)变换结合起来解决遥感图像融合的问题。具体来说:我们对全色波段图像进行二维BEMD分解,提取图像不同频率的信息,并结合IHS变换将光谱信息和图像细节信息叠合到融合图像上,使所产生的新图像保持了原来图像的多光谱特性并具有较高的空间分辨率。随后我们提出了一种完全重构的图像解调算法。图像解调算法是用图像的瞬时振幅、瞬时相位、瞬时频率等重要特征来表示图像。鉴于瞬时频率等特征对单成分信号才有意义,我们首先分解图像得到图像的每个单成分。传统的分解方法大都采用Gabor滤波器来提取图像在某个固定频带的成分,且分解的结果不能重构原信号。与此不同,BEMD是一种自适应的分解方法,并且由BEMD分解得到的单成分可以完全重构原图像。我们利用BEMD方法分解图像,然后对提取的单成分利用四元数解析的方法得到二维解析信号。四元数解析方法符合二维解析的推广条件,是一种合适的解析方法。我们还采用一种新的极坐标表示形式,提取了图像的瞬时振幅、瞬时相位、瞬时频率等特征,达到了图像解调的目的。该方法还是一种完全重构的图像解调算法。随后我们还利用提取的特征进行了图像分割实验,实验效果较好,这也进一步验证了该图像解调算法的有效性。最后,通过计算二维瞬时频率,我们发现二维EMD具有类似二进滤波器的性质并提供了一种分离图像的方法。利用本文提出的二维瞬时频率的计算方法,我们计算了不同图像的瞬时频率向量的模,画出了图像的每个IMF的瞬时频率向量模的分布图并计算了瞬时频率向量模的均值。实验结果可以看出二维EMD具有类似二进滤波器的性质,这一结论与一维EMD的结论类似。本文的研究首次反映了二维EMD的性质,也表明二维瞬时频率可以为二维HHT的研究提供新的思路。此外,我们将瞬时频率作为判别条件分离图像,将图像分解为纹理部分和光滑部分。通过这种分离方法,图像的不同部分可以采用不同的图像压缩方式,这为图像压缩提供了便利条件。更多还原

【Abstract】 As an important branch of signal processing, image processing has become a hot researchspot. It has many applications, such as video image processing, medical image processing, re-mote sensing image processing and so on. Image processing has developed a lot of branches,including image fusion、image segmentation、texture analysis、image compression. The de-velopment of image processing depends on the development of signal processing technology.The traditional signal processing methods include Fourier transform, wavelet analysisand Wigner distribution et al. Huang et al. proposed a new data analysis methods - Hilbert-Huang transform in 1998. Completely different with the traditional method, HHT methoddoes not require any basis function. It is an adaptive time-frequency analysis method. First,the base function is obtained adaptively from the Empirical Mode Decomposition. The re-sults of the decomposition are the intrinsic mode functions (IMF).Then, the analytic signal isobtained by calculating the Hilbert transform of the IMF. The instantaneous frequency is gotby the derivative of the phase of the analytic signal. The Hilbert spectrum is obtained in thetime - frequency - amplitude plane. HHT method is especially suitable for nonlinear signalanalysis, and it has been successfully applied in medical, military, oceanography and manyother important areas.In view of these advantages, the two-dimensional HHT method has been widespreadconcerned. People begin to study the two-dimensional EMD decomposition algorithm, andachieved many results. However, as the complexity of two-dimensional signals, there are stillmany problems to be studied.In this paper, the theory of two-dimensional HHT method and its applications in imageprocessing have been studied. First of all, we study the two-dimensional EMD decompositionmethods、two-dimensional spectral feature extraction and other theoretical problems. Weimprove the existing two-dimensional decomposition method and obtain the instantaneousfrequency and other important features. Secondly, we apply the theory of two-dimensionalHHT in image processing, and have achieved some results. Definitely, the main works of thisarticle are as follows:In theoretical part, we improve the original two-dimensional EMD decomposition method and use the quaternion analytical method to extract the spectral characteristics of the two-dimensional IMF. First of all, as the computation time of BEMD is long, we adopt an im-proved BEMD method. We use the fast radial basis function in the extreme point interpola-tion, and use the mirror symmetry method in boundary processing. This method can speedup the iteration speed, and prohibit the boundary effect. We also conducte an in-depth studyin two-dimensional spectral features. The quaternion analytic approach has been proposed,and it is consistent with the two-dimensional analytical signal. Then using a new represen-tation form, we extract the two-dimensional IMFs’instantaneous amplitude、instantaneousphase、two instantaneous frequency、the three character of u. Then we do some experimentsfor both natural images and synthetic texture images. Experimental results show that thesefeatures can better re?ect the internal characteristics of the image and lay a theoretical basisfor the two-dimensional development of HHT.On the other hand, we apply the two-dimensional HHT method in image fusion andimage demodulation. We analyze the intrinsic characteristics of the two-dimensional EMDfor the first time. Then the two-dimensional instantaneous frequencies are applied to theimage separation successfully. We will describe the details separately.First, the two-dimensional BEMD and IHS Transform (Intensity-Hue-Saturation) is ap-plied to remote sensing image fusion. We use two-dimensional BEMD to decompose thepanchromatic band image, and extract the image details and textures of different frequencies.Combining with IHS transform, the spectral information and image detail information arecombined in the fusion images. The new images have both the multi-spectral characteristicsof the original image and a high spatial resolution.Then we propose a fully reconstructed image demodulation algorithm. Using the BEMDmethod,we extract the single component of the image. Different from the traditional Gabormethod, this decomposition method is an adaptive approach, and the original image can bereconstructed from the decomposition results. Then, the analytical signal is obtained by usingquaternion analytic methods. The quaternion analytic method fulfills most of the conditionsof two-dimensional analytical extension and is an appropriate analytical method. We alsointroduce a new polar representation, extract the instantaneous amplitude and the instanta- neous frequency. This method is also a fully reconstructed image demodulation algorithm. Inaddition, the image segmentation experiments verify the effectiveness of the method.Finally, we analyze the dynamic filter property of the two-dimensional EMD. Usingtwo-dimensional instantaneous frequency we provide an image separation method. In orderto analyze the nature of the two-dimensional EMD, we analyze different images. Makinguse of the two-dimensional instantaneous frequency property, we calculate the instantaneousfrequency’s modulus of the different IMF vectors and calculate the mean of the modulus ofthe instantaneous frequency vector. We can see the EMD in two dimensions has a similar dy-namic filter property, just as the conclusion of one-dimensional EMD. This method providesa new research method. In addition, the instantaneous frequency can be used as a criterion forimage separation. According to this separation method, the image can be decomposed intothe cartoon parts and smooth parts, then different parts can be compressed differently. Thismethod provides a convenient condition for the future research of HHT.更多还原