Optimal tree approximation with wavelets

Research output: Contribution to journalConference articlepeer-review

61 Scopus citations


The more a priori knowledge we encode into a signal processing algorithm, the better performance we can expect. In this paper, we overview several approaches to capturing the structure of singularities (edges, ridges, etc.) in wavelet-based signal processing schemes. Leveraging results from approximation theory, we discuss nonlinear approximations on trees and point out that an optimal tree approximant exists and is easily computed. The optimal tree approximation inspires a new hierarchical interpretation of the wavelet decomposition and a tree-based wavelet denoising algorithm that suppresses spurious noise bumps.

Original languageEnglish (US)
Pages (from-to)196-207
Number of pages12
JournalProceedings of SPIE - The International Society for Optical Engineering
StatePublished - Dec 1 1999
EventProceedings of the 1999 Wavelet Applications in Signal and Image Processing VII - Denver, CO, USA
Duration: Jul 19 1999Jul 23 1999

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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