The Statistical Restricted Isometry Property For Gabor Systems

摘要

Gabor matrices are important in many different areas of timefrequency analysis like radar or communications. For applications with sparse data, the question arises whether these matrices satisfy some recovery guarantees for compressive sampling, and which generating windows yield a matrix with restricted isometric property. This paper proves the uniqueness-guaranteed statistical restricted isometric property for Gabor matrices generated by an Alltop window. In that way, we present a recovery guarantee for this deterministic measurement matrix where the number of measurements scales linearly with the sparsity of the signals.