Optimal K dual frames and pairs in the presence of erasures

TL;DR

This paper investigates the structure of optimal K-dual frames and pairs to improve robustness against erasures in data transmission, focusing on minimizing error operator norms and spectral radius for better reconstruction.

Contribution

It introduces a comprehensive framework for designing optimal K-dual frames and pairs considering erasures, enhancing data recovery robustness in frame theory.

Findings

Optimal K-dual frames minimize reconstruction error under erasures.

Analysis of two erasure scenarios impacts on frame reconstruction.

Framework improves robustness in data transmission.

Abstract

This paper explores the structure of optimal K-dual frames for a given K-frame and optimal K-dual pairs, within the context of erasures which occur during the transmission of frame coefficients. We address two distinct erasure scenarios and examine their impact on the reconstruction process. The optimality criteria are defined in terms of minimizing the spectral radius and the operator norm of the associated error operators. Through this approach, we provide a comprehensive framework for understanding and mitigating the effects of erasures in frame theory, contributing to enhanced robustness in data transmission and recovery.