Quasi-Equiangular Frame (QEF) : A New Flexible Configuration of Frame

TL;DR

This paper introduces Quasi-Equiangular Frame (QEF), a flexible and practical alternative to ETF and Grassmannian Frames, with theoretical analysis and asymptotic properties relevant for signal processing applications.

Contribution

It formally defines QEF, analyzes its relation to existing frames, and provides asymptotic estimates of its Restricted Isometry Constant using random matrix techniques.

Findings

QEF offers a more flexible approximation to ETF and Grassmannian Frames.

Asymptotic concentration bounds for the RIC of QEF are derived.

QEF enhances robustness and performance in compressive sensing applications.

Abstract

Frame theory is a powerful tool in the domain of signal processing and communication. Among its numerous configurations, the ones which have drawn much attention recently are Equiangular Tight Frame (ETF) and Grassmannian Frame. These frames both have some kind of optimality in coherence, thus bring robustness or optimal performance in applications such as digital fingerprint, erasure channels, and Compressive Sensing. However, too strict constraint on existence and construction of ETF and Grassmannian Frame became the main obstacle for widespread use. In this paper, we propose a new configuration of frame: Quasi-Equiangular Frame, as a compromise but more convenient and flexible approximation of ETF and Grassmannian Frame. We will give formal definition of Quasi-Equiangular Frame and analyze its relationship with ETF and Grassmannian frame. Furthermore, for popularity of ETF and Grassmannian frame in Compressive Sensing, we utilize the technique of random matrices to obtain asymptotical concentration estimation of the Restricted Isometry Constant (RIC) of Quasi-Equiangular Frame with respect to its key parameter.