Eliminating distortion in the Beylkin-Coifman-Rokhlin transform

  • Authors:

  • John R. O'Hair;Bruce W. Suter

  • Affiliations:

  • Department of Electrical and Computer Engineering, Air Force Institute of Technology, Wright-Patterson AFB, OH;Department of Electrical and Computer Engineering, Air Force Institute of Technology, Wright-Patterson AFB, OH

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

Quantified Score

Hi-index 0.00

Visualization

Abstract

A systematic approach is presented for the elimination of distortion in the Beylkin-Coifman-Rokhlin (BCR) transform, a technique that requires only O(N) operations to apply an N × N matrix to an arbitrary vector. Since these matrices and vectors are of finite length, implementations of the BCR require the application of some extension technique, and these extension methods result in an additional O(N) non-zero terms. The resulting algorithm retains O(N) complexity while eliminating all distortion in a "perfect reconstruction" sense. The only distortion remaining is in the wavelet coefficients and that being due to the particular extension method chosen.