Sparse Matrices in Frame Theory

Jakob Lemvig, Felix Krahmer, Gitta Kutyniok

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Abstract

Frame theory is closely intertwined with signal processing through a canon of methodologies for the analysis of signals using (redundant) linear measurements. The canonical dual frame associated with a frame provides a means for reconstruction by a least squares approach, but other dual frames yield alternative reconstruction procedures. The novel paradigm of sparsity has recently entered the area of frame theory in various ways. Of those different sparsity perspectives, we will focus on the situations where frames and (not necessarily canonical) dual frames can be written as sparse matrices. The objective for this approach is to ensure not only low-complexity computations, but also high compressibility. We will discuss both existence results and explicit constructions.
Original languageEnglish
JournalComputational Statistics
Volume29
Issue number3-4
Pages (from-to)547-568
ISSN0943-4062
DOIs
Publication statusPublished - 2014

Keywords

  • Dual Frames
  • Frames
  • Redundancy
  • Signal Processing
  • Sparse Matrices
  • Tight Frames

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