An extension to the analytical Gabor expansion with applications in image coding

In this contribution we present an unified method that can be used to compute analytically the coefficients of the discrete non-orthogonal Gabor expansion for arbitrary type of orthogonal kernel. Based on the proposed algorithm an architecture is derived that enables a fast computation of modified time-frequency transforms such as Gabor-DCT. It will shown that for the special case of equidistant elementary cells the generalized Gabor transform can be modeled as a conventional block transform of modulated and filtered input signals. From this point of view it follows that the biorthogonal analysis window which is used in the modulation necessary for computation of the transform coefficients is independent of the selected orthogonal kernel. The problems caused by the non-stationarity of the modulated and filtered signal will be discussed and the coding performance and energy compaction of the classical Gabor transform, the Gabor-DCT, and the well known block DCT will be compared.