Geometric properties of Gabor frames with a random window

Abstract

In this paper we address various geometric properties of frames, such as spark, coherence, restricted isometry property, and frame order statistics. These properties play crucial role in various signal processing problems, including compressive sensing, phase retrieval, and quantization. We focus on a particular case of structured frames, namely on Gabor frames, where frame vectors are time and frequency shifts of a random window, and show that geometric properties of Gabor frames are close to optimum, which is usually demonstrated by Gaussian frames with independent vectors.