Reproducing kernel space based on GABOR wavelet transform

In this paper, the expression of the reproducing kernel function of image space of Gabor wavelet transform is shown based on the image space of the continuous wavelet transform as a reproducing kernel Hilbert space, and when scale factor and translation factor are fixed, a concrete characterization of image space of Gabor wavelet transform is given by the theory of reproducing kernel function. We obtain the isometrical identities and inversion formulae, which provides a new method for us to study the theory of image space of the general wavelet transform.