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On the Representation of Functions with Gaussian Wave Packets

In English

Författare

Summary, in English

Abstract in Undetermined
We introduce Gaussian wave packets in pursuit of representations of functions, in which the representation is invariant under translation, modulation, scale,
rotation and anisotropic dilation. Properties of both continuous and discrete representations are discussed. For the discrete (two-dimensional) case, we develop fast
algorithms for the application of the analysis and synthesis operators. A main objective for using Gaussian wave packets is to obtain sparse approximations of functions.
However, due to the many invariance properties, the representations will have a high
degree of redundancy. Therefore, we also introduce sparse methods for highly redundant representations, that employ some of the analytic properties of Gaussian wave
packet for gaining computational efficiency.

Publiceringsår

2012

Språk

Engelska

Sidor

146-181

Publikation/Tidskrift/Serie

Journal of Fourier Analysis and Applications

Volym

18

Dokumenttyp

Artikel i tidskrift

Förlag

Springer

Ämne

  • Mathematics
  • Computer Vision and Robotics (Autonomous Systems)

Nyckelord

  • Gaussian wave packets · Sparse representations · Fast algorithms · Compression

Status

Published

Forskningsgrupp

  • Harmonic Analysis and Applications

ISBN/ISSN/Övrigt

  • ISSN: 1531-5851