Frame Bounds for Gabor Frames in Finite Dimensions

Abstract

One of the key advantages of a frame compared to a basis is its redundancy. Provided we have a control on the frame bounds, this redundancy allows, among other things, to achieve robust reconstruction of a signal from its frame coefficients that are corrupted by noise, rounding error, or erasures. In this paper, we discuss frame bounds for Gabor frames (g, Λ) with generic frame set Λ and random window g. We show that, with high probability, such frames have frame bounds similar to the frame bounds of randomly generated frames with independent frame vectors.