The natural setting for time-frequency analysis and Gabor Analysis is the world of functions/signals or distributions over LCA (locally compact Abelian) groups $G$. A substantial part if the theory (the existence of a Janssen representation for the frame operator, etc.) has been developed in this context, making use of appropriate function spaces, in particular the Banach Gelfand Triple based on the Segal algebra $SO(G)$. In this setting only occasionally a distinction is made between the one-dimensional
or the multidimensional (e.g. Euclidean) setting.

In contrast, when it comes to implementation the situation changes. Not because Gabor analysis wasn't interesting for the multi-dimensional setting. In contrast, the first important papers in the field made the connection between Gabor expansions of images and the analogy with the visual system of humans. But in terms of available code the situation is rather satisfactory for the case of 1D-signals: one can compute dual or tight Gabor atoms, construct Gabor multipliers, and has cheap algorithms for a cheap (and efficient) determination of approximate versions of these objects.

The talk will discuss the obstacles and additional problem which arise from the large dimensions (the number of pixels of the involved images), the computational costs and above all the huge storage requirements. One possible way out (or at least a special family of Gabor expansions and Gabor multipliers which can be realized) is the use of separable Gabor families. We will also try to explain the relevance of the double preconditioning approach in the 2D-setting.