The Study Of Bidimensional Empirical Mode Decomposition And Applications In Image Processing

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.