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Nonstationary Gabor frames, recently introduced in adaptive signal analysis,represent a natural generalization of classical Gabor frames by allowing foradaptivity of windows and lattice in either time or frequency. Due to the lackof a complete lattice structure, perfect reconstruction is in general notfeasible from coefficients obtained from nonstationary Gabor frames. In thispaper it is shown that for nonstationary Gabor frames that are related to someknown frames for which dual frames can be computed, good approximatereconstruction can be achieved by resorting to approximately dual frames. Inparticular, we give constructive examples for so-called almost painlessnonstationary frames, that is, frames that are closely related to nonstationaryframes with compactly supported windows. The theoretical results areillustrated by concrete computational and numerical examples.

Nonstationary Gabor Frames - Approximately Dual Frames and Reconstruction Errors