On the Representation of Functions with Gaussian Wave Packets

Fredrik Andersson, Marcus Carlsson, Luis Tenorio

Research output: Contribution to journalArticlepeer-review

13 Citations (SciVal)

Abstract

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.
Original languageEnglish
Pages (from-to)146-181
JournalJournal of Fourier Analysis and Applications
Volume18
DOIs
Publication statusPublished - 2012

Subject classification (UKÄ)

  • Mathematics
  • Computer Vision and Robotics (Autonomous Systems)

Keywords

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

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