Non-orthogonal Fusion Frames and the Sparsity of Fusion Frame Operators View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2012-04

AUTHORS

Jameson Cahill, Peter G. Casazza, Shidong Li

ABSTRACT

Fusion frames have become a major tool in the implementation of distributed systems. The effectiveness of fusion frame applications in distributed systems is reflected in the efficiency of the end fusion process. This in turn is reflected in the efficiency of the inversion of the fusion frame operator , which in turn is heavily dependent on the sparsity of . We will show that sparsity of the fusion frame operator naturally exists by introducing a notion of non-orthogonal fusion frames. We show that for a fusion frame {Wi,vi}i∈I, if dim(Wi)=ki, then the matrix of the non-orthogonal fusion frame operator has in its corresponding location at most a ki×ki block matrix. We provide necessary and sufficient conditions for which the new fusion frame operator is diagonal and/or a multiple of an identity. A set of other critical questions are also addressed. A scheme of multiple fusion frames whose corresponding fusion frame operator becomes an diagonal operator is also examined. More... »

PAGES

287-308

References to SciGraph publications

  • 2011-07. Sparse fusion frames: existence and construction in ADVANCES IN COMPUTATIONAL MATHEMATICS
  • 2009-07. Frame Fundamental Sensor Modeling and Stability of One-Sided Frame Perturbation in ACTA APPLICANDAE MATHEMATICAE
  • 2004-07. Pseudoframes for Subspaces with Applications in JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
  • 2010-08. The Structure of Minimizers of the Frame Potential on Fusion Frames in JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
  • 2008-02. Optimal noise suppression: A geometric nature of pseudoframes for subspaces in ADVANCES IN COMPUTATIONAL MATHEMATICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00041-011-9200-7

    DOI

    http://dx.doi.org/10.1007/s00041-011-9200-7

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1000454278


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