Title

Optimal Dual Frames For Erasures

Keywords

46C05; 47B10; Erasures; Frames; Optimal dual frames; Primary 42C15

Abstract

For any given frame (for the purpose of encoding) in a finite dimensional Hilbert space, we investigate its dual frames that are optimal for erasures (for the purpose of decoding). We show that in general the canonical dual is not necessarily optimal. Moreover, optimal dual frames are not necessarily unique. We present some sufficient conditions under which the canonical dual is the unique optimal dual frame for the erasure problem. As an application, we get that the canonical dual is the only optimal dual when either the frame is induced by a group representation or the frame is uniform tight. © 2009 Elsevier Inc. All rights reserved.

Publication Date

1-1-2010

Publication Title

Linear Algebra and Its Applications

Volume

432

Issue

1

Number of Pages

471-482

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.laa.2009.08.031

Socpus ID

70449530518 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/70449530518

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