Convolutional Frames and the Frame Potential
The recently introduced notion of frame potential has proven useful for the characterization of finite-dimensional tight frames. The present work represents an effort to similarly characterize finite-dimensional tight frames with additional imposed structure. In particular, it is shown that the frame potential still leads to a complete description of tight frames when restricted to the class of translation-invariant systems. It is natural to refer to such frames as convolutional because of the correspondence between translation-invariant systems and finite-dimensional filter banks. The fast algorithms associated with convolution represent one possible advantage over nonconvolutional frames in applications.
Abstract © Elsevier
Applied and Computational Harmonic Analysis
Fickus, M., Johnson, B. D., Kornelson, K., & Okoudjou, K. A. (2005). Convolutional frames and the frame potential. Applied and Computational Harmonic Analysis, 19(1), 77–91. https://doi.org/10.1016/j.acha.2005.02.005