Optimal dual pairs of frames for erasures

TL;DR

This paper characterizes and constructs optimal dual pairs of frames in finite-dimensional Hilbert spaces for erasure resilience, introducing new optimality measures and analyzing their performance under multiple erasures.

Contribution

It introduces a new Frobenius norm-based optimality measure for dual frames and provides explicit constructions for optimal dual pairs under erasures.

Findings

Optimal dual pairs minimize error operator norms under erasures.

New Frobenius norm-based optimality measure introduced.

Explicit constructions of optimal dual pairs provided.

Abstract

The study involves characterizations of dual pairs of frames which are optimal to handle erasures among all dual pairs for a finite dimensional Hilbert space. A new optimality measure using the Frobenius norm of the error operator has been introduced and the corresponding optimal dual pairs have been analyzed for any number of erasures. Also, other measures of the error operator, namely the spectral radius and the numerical radius, have been considered for the analysis. Besides, explicit construction of certain optimal dual pairs has been provided.