Signal- and image-component separation by a multi-window Gabor-type scheme

The discrete (finite) Gabor scheme is generalized by incorporating multi-windows. Two approaches are presented for the analysis of the generalized scheme: the signal domain approach and Zak transform domain approach. These approaches are based on representing the frame operator as a matrix-valued function, and are far less demanding from a computational complexity viewpoint than a straightforward matrix algebra in various operations such as the computation of the dual frame. Issues related to undersampling, critical sampling and oversampling are considered. Examples illustrating the advantages of the multi-window scheme over the single-window scheme are presented