Linearly connected sequences and spectrally optimal dual frames for erasures

    Authors

    S. Pehlivan; D. G. Han;R. Mohapatra

    Comments

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    Abbreviated Journal Title

    J. Funct. Anal.

    Keywords

    Frames; Erasures; Spectrally optimal dual frames; Connected frames; Redundancy distribution; k-independent sets; EQUIANGULAR TIGHT FRAMES; SEIDEL MATRICES; PARSEVAL FRAMES; REPRESENTATIONS; COMMUNICATION; Mathematics

    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. (C) 2013 Elsevier Inc. All rights reserved.

    Journal Title

    Journal of Functional Analysis

    Volume

    265

    Issue/Number

    11

    Publication Date

    1-1-2013

    Document Type

    Article

    Language

    English

    First Page

    2855

    Last Page

    2876

    WOS Identifier

    WOS:000324603100008

    ISSN

    0022-1236

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