New constructions of piecewise-constant wavelets

Hur Youngmi, Ron Amos

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


The classical Haar wavelet system of L2(ℝn) is commonly considered to be very local in space. We introduce and study in this paper piecewise-constant framelets (PCF) that include the Haar system as a special case, We show that any bi-framelet pair consisting of PCFs provides the same Besov space characterizations as the Haar system. In particular, it has Jackson-type performance S J = 1 and Bernstein-type performance SB = 0.5. We then construct two PCF systems that are either, in high spatial dimensions, far more local than Haar, or are as local as Haar while delivering better performance: SJ = SB = 1. Both representations are computed and inverted by fast algorithms.

Original languageEnglish
Pages (from-to)138-157
Number of pages20
JournalElectronic Transactions on Numerical Analysis
Publication statusPublished - 2006

All Science Journal Classification (ASJC) codes

  • Analysis


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