Bidimensional Empirical Mode Decomposition Method And Its Application Research In Image Processing

The empirical mode decomposition (EMD) introduced by Norden E Huang is a new multi-scale analysis method. It is suitable for non-linear and non-stationary signal processing. It is considered an important breakthrough for non-stationary signal analysis methods which are based on Fourier transform. On account of the EMD method has good effects in one-dimensional signal processing, and scholars extend it to bidimensional. They introduce some bidimensional empirical mode decomposition (BEMD) methods, and process bidimensional signal with these BEMD. Because of the complexity in bidimensional signal, the general BEMD have many defects need to be researched.The dissertation studies two aspects of BEMD method. One is the problem existing in the theory aspect; the other is the problem in the practical application, and the main analysis research object is two-dimensional image signal. Main works of the dissertation are as follows:1. In this dissertation, we analyze the BEMD method which is introduced by J. C. Nunes et al. The implement approaches are given. The multi-scale decompositions are completed for a great deal experimentation well and truly.2. Research contrastively two crucial taches of the BEMD method, identifying the extrema and generating the 2D'envelope'by connecting maxima points (respectively, minima points). The methods to solve the border problem are proposed. Analyze and compare the shortcomings of Delaunay triangulation and radial basis function interpolation. The BEMD method to combine two interpolation methods is suggested on account of their own characteristic.3. The modified BEMD method in this dissertation is introduced to process the images with high resolution ratio based on the radial basis function interpolation method. The image is split into several blocks, and every block is processed individually. Then they are oversewed by natural image mosaicing technique. So we can get ride of solving large linear equations and calculating huge matrix. It is proved that the modified method has high a calculating speed and solves the border problem as a result of blocking. Considering the fact of this arithmetic, we give a new criterion for the sifting process to stop.4. We attempt to apply BEMD to image processing, including texture analysis and noise reduction. At the same time, in virtue of characteristic of the intrinsic mode function (IMF), a new image compression thought is proposed based BEMD, which only extract and transfer extrema (both maxima and minima) and zero-crossings. The experiments prove that this method is feasible.