A 'nondecimated' lifting transform

MI Knight, GP Nason

Research output: Contribution to journalArticle (Academic Journal)

7 Citations (Scopus)

Abstract

Classical nondecimated wavelet transforms are attractive for many applications. When the data comes from complex or irregular designs, the use of second generation wavelets in nonparametric regression has proved superior to that of classical wavelets. However, the construction of a nondecimated second generation wavelet transform is not obvious. In this paper we propose a new ‘nondecimated’ lifting transform, based on the lifting algorithm which removes one coefficient at a time, and explore its behavior. Our approach also allows for embedding adaptivity in the transform, i.e. wavelet functions can be constructed such that their smoothness adjusts to the local properties of the signal. We address the problem of nonparametric regression and propose an (averaged) estimator obtained by using our nondecimated lifting technique teamed with empirical Bayes shrinkage. Simulations show that our proposed method has higher performance than competing techniques able to work on irregular data. Our construction also opens avenues for generating a ‘best’ representation, which we shall explore.
Translated title of the contributionA 'nondecimated' lifting transform
Original languageEnglish
Pages (from-to)1 - 16
Number of pages16
JournalStatistics and Computing
Volume19
Issue number1
DOIs
Publication statusPublished - Mar 2009

Bibliographical note

Publisher: Springer

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