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Sparse matrices in frame theory

Author

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  • Felix Krahmer
  • Gitta Kutyniok
  • Jakob Lemvig

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. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Felix Krahmer & Gitta Kutyniok & Jakob Lemvig, 2014. "Sparse matrices in frame theory," Computational Statistics, Springer, vol. 29(3), pages 547-568, June.
    • Handle: RePEc:spr:compst:v:29:y:2014:i:3:p:547-568
    DOI: 10.1007/s00180-013-0446-1
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    Cited by:

    1. Nickolay Trendafilov & Martin Kleinsteuber & Hui Zou, 2014. "Sparse matrices in data analysis," Computational Statistics, Springer, vol. 29(3), pages 403-405, June.

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