A class of wavelet kernels associated with wave propagation

Wavelet kernels in the form of complex exponentials with linear instantaneous frequencies are discussed. These wavelets do not satisfy the commonly used admissibility condition; furthermore, they are neither band-, nor space-limited functions and they are not absolutely integrable. It is shown, however, that the wavelet transforms using these kernels are still invertable and the inversion formulas are given. Such kernels are closely related to wave propagation related phenomena like the diffraction and the holography, and therefore, the obtained mathematical results coincide to well known optical applications. The kernels may be useful in space-depth analysis of data obtained from diffraction related imaging techniques