Characterization of Oblique Dual Frame Pairs

Ole Christensen, Yonina Eldar

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    Given a frame for a subspace W of a Hilbert space H, we consider all possible families of oblique dual frame vectors on an appropriately chosen subspace V. In place of the standard description, which involves computing the pseudoinverse of the frame operator, we develop an alternative characterization which in some cases can be computationally more efficient. We first treat the case of a general frame on an arbitrary Hilbert space, and then specialize the results to shift-invariant frames with multiple generators. In particular, we present explicit versions of our general conditions for the case of shift-invariant spaces with a single generator. The theory is also adapted to the standard frame setting in which the original and dual frames are defined on the same space. Copyright (C) 2006 Hindawi Publishing Corporation. All rights reserved.
    Original languageEnglish
    JournalEURASIP Journal on Applied Signal Processing
    Pages (from-to)1-11
    ISSN1110-8657
    DOIs
    Publication statusPublished - 27 Apr 2006

    Bibliographical note

    Article ID 92674

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