  We propose Fourier transform (FT) method for processing images of extensive
air showers (EAS) detected by imaging atmospheric Cherenkov telescopes (IACT)
used in the very high energy (VHE) gamma-ray astronomy. The method is based on
the discrete Fourier transforms (DFT) on compact Lie groups, and the use of
continuous extension of the inverse discrete transforms to approximate the
discrete EAS images by continuous EAS brightness distribution functions. Here
we describe the FT-method in case of SU(3) group. It allows practical
realization of the DFT technique for functions sampled on hexagonal symmetry
grids. The proposed method can also be implemented in case of IACT cameras with
grids of rectangular symmetry by using the DFT on the SU(2)xSU(2) group. The
proposed FT-method is applied to the Monte-Carlo simulated bank of TeV proton
and gamma-ray EAS images for a stand-alone telescope. Comparing between the
FT-method and the currently used standard method shows that the FT technique
allows a better and systematic enhancement of the gamma-ray signal. The
relative difference between these two methods becomes more profound especially
for `photon poor' images. It suggests that the EAS detection thresholds of
IACTs could be effectively reduced with the use of FT technique. This
prediction is further supported by a significant noise suppression capability
of the method using simple low-pass filters in the image frequency domain. The
FT-method allows very deep `tail' (and `height') image cuts, differentiation of
images, operations in the image frequency domain, etc., that can be used for
development of new effective parameters for the EAS image processing.
