Bidimensional Empirical Mode Decomposition In Image Processing

Empirical Mode Decomposition (EMD) is a new technology of signal processing, which is used in many fields such as seismology, oceanography, medicine, economics, phonetics, mechanical failure analysis. EMD is based on the direct extraction of the energy associated with various intrinsic time scales. Expressed in Intrinsic Mode Functions (IMFs), they have well-behaved Hilbert transforms, from which the instantaneous frequencies can be calculated. Thus, any event can be localized on the time as well as the frequency axis. EMD can also be viewed as an expansion of the data in terms of the IMFs. Then, these IMFs, based on and derived from the data, can serve as the basis of that expansion which can be linear or nonlinear as dictated by the data. It is a local and adaptive method in frequency-time analysis. EMD is the effective use of the data. The most important conceptual innovations of the present study are the physical significance assigned to the instantaneous frequency for each mode of a complicated data set, and the introduction of the IMF.Bidimensional Empirical Mode Decomposition (BEMD) is a new form of multi-scale structure. Though BEMD is a rising technology, there are some difficult problems, such as the costly computation and storage in order to extract the envelopes with Radial Basis Function (RBF), and boundary effect of BEMD. There are many methods to interpolate surface from scattered data. However these methods have some limitations, such as the smoothness, the computation or the data distribution. Suppressing the boundary effect is a key to BEMD. When we sift the data, if there are data dispersal at the end of upper and low envelopes, the dispersal will gradually runs inside the series of data and 'pollutes' the whole data as sifting.In this paper, a method is proposed which uses the periodic RBF to improve the BEMD. The choice of interpolation function and suppressing the boundary effect are the key problems of BEMD. The mirror periodic compactly supported Radial Basis Function not only has the precision of interpolation and suppresses the boundary effect, but also has fast computation. Experiments indicate that the method in this paper can gain better decompositions.