Grassmannian Fusion Frames

TL;DR

This paper introduces a new construction of Grassmannian fusion frames, combining concepts from Grassmannian frames and fusion frame theory, with potential applications in distributed sensing and data transmission robustness.

Contribution

It presents a simple, novel method for constructing Grassmannian fusion frames and extends this to include local frames, linking to sparse representations.

Findings

New construction method for Grassmannian fusion frames

Extension to Grassmannian fusion frames with local frames

Discussion of connections to sparse representations

Abstract

Transmitted data may be corrupted by both noise and data loss. Grassmannian frames are in some sense optimal representations of data transmitted over a noisy channel that may lose some of the transmitted coefficients. Fusion frame (or frame of subspaces) theory is a new area that has potential to be applied to problems in such fields as distributed sensing and parallel processing. Grassmannian fusion frames combine elements from both theories. A simple, novel construction of Grassmannian fusion frames with an extension to Grassmannian fusion frames with local frames shall be presented. Some connections to sparse representations shall also be discussed.