Duality in reconstruction systems

TL;DR

This paper explores the mathematical structure of finite-dimensional reconstruction systems, including fusion frames, analyzing dual systems, spectral properties, and optimization of joint potentials.

Contribution

It introduces new geometric and spectral insights into reconstruction systems, extending understanding of duals and optimization in this framework.

Findings

Characterization of dual systems and their spectral properties

Analysis of the set of RS operators for fixed weights

Identification of minimizers of the joint potential

Abstract

We consider the notion of finite dimensional reconstructions systems (RS's), which includes the fusion frames as projective RS's. We study erasures, some geometrical properties of these spaces, the spectral picture of the set of all dual systems of a fixed RS, the spectral picture of the set of RS operators for the projective systems with fixed weights and the structure of the minimizers of the joint potential in this setting. We give several examples.