Reproducing Kernel Function Of Image Space Of Journe Wavelet Transform

The researches of theory and application of wavelet analysis have acquired plentiful and substantial results. And the theory and application of wavelet analysis have been widely applied to many fields, such as signal and information processing, image processing, seismic exploration, speech recognition, CT image formation, and so on. With the rise of wavelet the theory of the reproducing kernel attracts more and more scholars'attention in some fields because reproducing kernel Hilbert space is the basis of continue wavelet transform and it is very important for us to reconstruct the continue wavelet transform. In this paper the reproducing kernel function and the properties of image space of Journe wavelet transform are shown by virtue of the special fact that the image space of the wavelet transform is a reproducing kernel Hilbert space. Meanwhile, the related properties of the reproducing kernel in the form of the matrix are given.Firstly, the expression of the reproducing kernel function and the isometric identity of image space of Journe wavelet transform are shown based on the fact that the image space of wavelet transform is a reproducing kernel Hilbert space, and the connections between the image space of Journe wavelet transform and the known reproducing kernel Hilbert space are established by the theory of reproducing kernel Hilbert space. The properties of image space of Journe wavelet transform can be characterized by the properties of image space of the known reproducing kernel Hilbert space. Meanwhile, the sampling formula and the truncation error estimation of image space of wavelet transform are given. By the ideas of reproducing kernel we can try to consider the relations between the wavelet transform and sampling theorem. It will be an elementary attempt for us to discuss the issues of wavelet analysis by theory of reproducing kernel Hilbert space. This provides theoretical basis for us to further study the image space of the general wavelet transform and it develops the applied fields of theory of the reproducing kernel Hilbert space.Secondly, the properties of related reproducing kernel Hilbert spaces are considered by the reproducing kernel in the form of matrix. This provides a new method for solving the expression of Bergman kernel function.