Multiresolution analysis frames with applications

  • Authors:

  • John J. Benedetto;Shidong Li

  • Affiliations:

  • Department of Mathematics, University of Maryland, College Park, MD;Department of Applied Mathematics and Statistics, University of Maryland, Baltimore, MD

  • Venue:
  • ICASSP'93 Proceedings of the 1993 IEEE international conference on Acoustics, speech, and signal processing: digital speech processing - Volume III
  • Year:
  • 1993

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Abstract

A generalization of Multiresolution Analysis (MRA) to arbitrary affine frames, and the constructions of affine frames based on MRAs are considered and characterized. We define a Frame Multiresolution Analysis (FMRA), and provide a necessary and sufficient condition for constructing frames of translates. We derive conditions for constructing FMRAs and associated frames. The results are part of the theoretical background for multiscale signal processing problems including filter bank design, where redundancy and robustness play a role.