Quasi-Equiangular Frames (QEFS): A new flexible configuration of frames

Various structures and configurations make frame to be a powerful tool in the domain of signal processing. Among its numerous configurations, the ones which have drawn much attention recently are Equiangular Tight Frames (ETFs) and Grassmannian Frames. These frames both have optimality in coherence, thus bring robustness and optimal performance in applications such as digital fingerprint, erasure channels, and Compressive Sensing. However, the strict constraint on existence and construction of ETFs and Grassmannian Frames becomes the main obstacle for widespread use. In this paper, we propose a new configuration of frames: Quasi-Equiangular Frames, as a compromise but more convenient and flexible approximation of ETFs and Grassmannian Frames. We will give formal definition of Quasi-Equiangular Frames and analyze its relationship with ETFs and Grassmannian Frames. Furthermore, for popularity of ETFs and Grassmannian Frames in Compressive Sensing, we utilize the technique of random matrices to obtain a probabilistic bound for the Restricted fsometry Constant (RfC) of Quasi-Equiangular Frame. Numerical simulations are demonstrated for validation.