Double Preconditioning for the Gabor Frame Operator

We present an application of the idea of preconditioning in the context of Gabor frames. We propose a method to find an approximation for the inversion of the Gabor frame operator, based on (double) preconditioning. We thereby obtain very good approximations of the true dual Gabor atom at very low computational costs. Part of the efficiency of the proposed scheme results from the fact that all the matrices involved share a well-known block matrix structure. For Gabor atoms typically used in applications, the combination of these two preconditioners leads to very good results