Signal recovery and frames that are robust to erasure

TL;DR

This paper explores the use of highly redundant finite frames for robust signal recovery despite random erasures, leveraging random matrix theory and operator Khintchine inequalities for improved accuracy.

Contribution

It introduces a novel approach combining high-redundancy frames and advanced inequalities to enhance signal recovery robustness against data loss.

Findings

High redundancy frames enable recovery after 50% random erasures.

Random matrix theory underpins the recovery guarantees.

Operator Khintchine inequality improves sparse matrix signal recovery.

Abstract

We consider finite frames with high redundancy so that if half the terms transmitted from the sender are randomly deleted during transmission, then on average, the receiver can still recover the signal to within a high level of accuracy. This follows from a result in random matrix theory. We also give an application of the operator Khintchine inequality in the setting of signal recovery when the signal is a matrix with a sparse representation.