Construction of Fusion Frame Systems in Finite Dimensional Hilbert Spaces

Abstract

We first investigate the construction of a fusion frame system in a finite-dimensional Hilbert space ${𝔽}^n$ when its fusion frame operator matrix is given and provides a corresponding algorithm. The matrix representations of its local frame operators and inverse frame operators are naturally obtained. We then study the related properties of the constructed fusion frame systems. Finally, we implement the construction of fusion frame systems which behave optimally for erasures in some special sense in signal transmission.