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On the Representation of Functions with Gaussian Wave Packets

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Author

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.

Publishing year

2012

Language

English

Pages

146-181

Publication/Series

Journal of Fourier Analysis and Applications

Volume

18

Document type

Journal article

Publisher

Springer

Topic

  • Mathematics
  • Computer Vision and Robotics (Autonomous Systems)

Keywords

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

Status

Published

Research group

  • Harmonic Analysis and Applications

ISBN/ISSN/Other

  • ISSN: 1531-5851