A generalized non-separable 2-D discrete Gabor expansion for image representation and compression

We present a theory of generalized non-separable two dimensional (2-D) discrete Gabor expansions (DGE). We show that a DGE is essentially a general frame decomposition. Using this theory, we show that a non-separable 2-D analysis sequence can also be the translation and modulation of a single 2-D function γ. A novel algorithm for computing all possible nonseparable 2-D γ is also derived. The non-separable 2-D DGE scheme is useful, e.g., in applications where the orientation of the 2-D Gabor analysis window is important