Two Dimensional Hilbert-Huang Transform And Its Application In Image Processing

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.