Optimal representation of piecewise Holder smooth bivariate functions by the Easy Path Wavelet Transform

JOURNAL OF APPROXIMATION THEORY

卷:176

Article

Plonka, Gerlind¹  Iske, Armin²  Tenorth, Stefanie¹ 

[1] Univ Gottingen, Inst Numer & Appl Math, D-37083 Gottingen, Germany

[2] Univ Hamburg, Dept Math, D-20146 Hamburg, Germany

关键词: Sparse data representation;    Wavelet transform along pathways;    N-term approximation;   

DOI  :  10.1016/j.jat.2013.08.002

来源: Elsevier

【 摘 要 】

The Easy Path Wavelet Transform (EPWT) (Plonka, 2009) [26] has recently been proposed by one of the authors as a tool for sparse representations of bivariate functions from discrete data, in particular from image data. The EPWT is a locally adaptive wavelet transform. It works along pathways through the array of function values and it exploits the local correlations of the given data in a simple appropriate manner. In this paper, we aim to provide a theoretical understanding of the performance of the EPWT. In particular, we derive conditions for the path vectors of the EPWT that need to be met in order to achieve optimal N-term approximations for piecewise Holder smooth functions with singularities along curves. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free