Title

Linearly Connected Sequences And Spectrally Optimal Dual Frames For Erasures

Keywords

Connected frames; Erasures; Frames; K-independent sets; Redundancy distribution; Spectrally optimal dual frames

Abstract

In the case that a frame is prescribed for applications and erasures occur in the process of data transmissions, we examine optimal dual frames for the recovery from single erasures. In contrast to earlier papers, we consider the spectral radius of the error operator instead of its operator norm as a measure of optimality. This notion of optimality is natural when the Neumann series is used to recover the original data in an iterative manner. We obtain a complete characterization of spectrally one-erasure optimal dual frames in terms of the redundancy distribution of the prescribed frame. Our characterization relies on the connection between erasure optimal frames and the linear connectivity property of the frame. We prove that the linear connectivity property is equivalent to the intersection dependent property, and is also closely related to the well-known concept of a k-independent set. Additionally, we also establish several necessary and sufficient conditions for the existence of an alternate dual frame to make the iterative reconstruction work. © 2013 Elsevier Inc.

Publication Date

12-1-2013

Publication Title

Journal of Functional Analysis

Volume

265

Issue

11

Number of Pages

2855-2876

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jfa.2013.08.012

Socpus ID

84883756377 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84883756377

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