Directional Haar wavelet frames on triangles

被引：20

作者：

Krommweh, Jens ^{[1
]}

Plonka, Gerlind ^{[1
]}

机构：

[1] Univ Duisburg Essen, Dept Math, D-47048 Duisburg, Germany

来源：

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS | 2009年 / 27卷 / 02期

关键词：

Haar wavelet frames; Non-separable wavelets; Composite dilation wavelets; Dual frames; Sparse representation; Image denoising; PIECEWISE-CONSTANT WAVELETS; CONTOURLET TRANSFORM; IMAGE COMPRESSION; REPRESENTATION; TRIANGULATIONS; APPROXIMATION;

D O I：

10.1016/j.acha.2009.03.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Traditional wavelets are not very effective in dealing with images that contain orientated discontinuities (edges). To achieve a more efficient representation one has to use basis elements with much higher directional sensitivity. In recent years several approaches like curvelets and shearlets have been studied providing essentially optimal approximation properties for images that are piecewise smooth and have discontinuities along Cl-curves. While curvelets and shearlets have compact support in frequency domain, we construct directional wavelet frames generated by functions with compact support in time domain. Our Haar wavelet constructions can be seen as special composite dilation wavelets, being based on a generalized multiresolution analysis (MRA) associated with a dilation matrix and a finite collection of 'shear' matrices. The complete system of constructed wavelet functions forms a Parseval frame. Based on this MRA structure we provide an efficient filter bank algorithm. The freedom obtained by the redundancy of the applied Haar functions will be used for an efficient sparse representation of piecewise constant images as well as for image denoising. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：215 / 234

页数：20

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