Window Empirical Mode Decomposition And Its Application In Image Processing

Empirical Mode Decomposition (EMD) is a new technology of signal processing. EMD can decompose the nonlinear and non-stationary signals into a series of intrinsic mode functions (IMF) which has local oscillation mode of every point in time/space domain. After Hilbert transformation, the obtained instrantaneous frequency data will give a better understanding of the physics. Fourier transformation can obtain a better resolution in the frequency domain, but not in the time/space domain. Window Fourier transformation can only obtain a limited time/space-frequency resolution, because window function is fixed. Wavelet transformation has capability of multi-scale and multi-resolution, and can obtain a better resolution simultaneously in the time/space and frequency domains at different scales. However, because the basic function is fixed, it is disadvantageous to the results of analysis. EMD is based on the local characteristic time scale of the data. Compared with wavelet, EMD has all advantages of wavelets, and dispels the drawback of wavelets, so IMF can accurately reflect physical characteristics of the signals. Therefore, Hilbert-Huang transformation is superior to Fourier and wavelet.The drawback of EMD algorithm is inevitable, because EMD algorithm is based on experience. First,Calculating speed of EMD is very slow; Second,EMD can't resolve "information hiding" problem, which is that two mixed signals with great frequency difference can't be separated under certain conditions. They will influence the area of application in image processing. A new EMD algorithm---Window Empirical Mode Decomposition (WEMD) is proposed to solve problems. The experiments indicate that the new algorithm is superior to the existing algorithms. After the new algorithm is applied to digital image processing, the results show that they have the potential in digital image processing fields.The main innovation and work are: 1. For solving the drawbacks in 2D-EMD, new method of EMD...WEMD based on the window function and on the EMD's frame is proposed. The WEMD possesses both advantages:first, the algorithm possesses high calculating speed; second, the algorithm has solved the "information hiding" problem, which is difficult to be solved in traditional EMD algorithm.2. The IMF images of the traditional 2-D EMD algorithm are inevitable to produce gray spots for "signal hiding", so its field of application is limited. My thesis will utilize WEMD's ability in the acquirement of the high frequency data and its capability of multi-scale and multi-resolution to study the algorithms in digital image applications:A. Image edge extraction:Two methods of edge extraction are proposed by making use of the characteristic of the first IMF image which has the good edge. One utilizes the threshold to extact the edge; the other utilizes the Hilbert transformation and non-maxima suppression to extact the edge.B. Image fusion:The ability in the acquirement of the high frequency data and the capability of multi-scale and multi-resolution of WEMD are uitilized. After modifying the IMF components with the proposed fusion rule, the fusion image can be obtained by adding up the modified IMFs and the residual component.C. Image denoising:Because the noise in IMF images represents speckle noise, Gammma filter is applied to modify the IMF components. The denoise image can be obtained by adding up the modified IMFs and the residual component.D. Image enhancement:For the histogram of IMF image following normal distribution, the first few IMF images may be modified by histogram matching to enhance the IMF images. The enhanced image will be obtained by adding up the modified IMFs and the residual component. The experiments have shown that the proposed algorithms are efficient in image processing and better than the existing algorithms.3. According to EMD's frame and the cryptographic thinking, the SD value which is the sift stop condition of every IMF is as key. After the every IMF will be obtained by utilizing the different SD, one IMF will be replaced with secret image of equal size. The image with secret image will be obtained by adding up the IMFs and the residual component. When secret image needs to be restored, it may be restored.