The Easy Path Wavelet Transform: A New Adaptive Wavelet Transform for Sparse Representation of Two-Dimensional Data

IF 1.9 4区数学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Multiscale Modeling & Simulation Pub Date : 2009-04-03 DOI:10.1137/080719248

G. Plonka

引用次数: 86

Abstract

We introduce a new locally adaptive wavelet transform, called easy path wavelet transform (EPWT), that works along pathways through the array of function values and exploits the local correlations of the data in a simple appropriate manner. The usual discrete orthogonal and biorthogonal wavelet transform can be formulated in this approach. The EPWT can be incorporated into a multiresolution analysis structure and generates data dependent scaling spaces and wavelet spaces. Numerical results show the enormous efficiency of the EPWT for representation of two-dimensional data.

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简单路径小波变换:二维数据稀疏表示的一种新的自适应小波变换

我们引入了一种新的局部自适应小波变换，称为易路径小波变换(EPWT)，它沿着函数值数组的路径工作，并以一种简单适当的方式利用数据的局部相关性。常用的离散正交和双正交小波变换可以用这种方法表示。EPWT可以集成到多分辨率分析结构中，并生成与数据相关的尺度空间和小波空间。数值结果表明，EPWT对二维数据的表示具有极大的效率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Multiscale Modeling & Simulation 数学-数学跨学科应用

CiteScore

2.80

自引率

6.20%

发文量

审稿时长

6-12 weeks

期刊介绍： Centered around multiscale phenomena, Multiscale Modeling and Simulation (MMS) is an interdisciplinary journal focusing on the fundamental modeling and computational principles underlying various multiscale methods. By its nature, multiscale modeling is highly interdisciplinary, with developments occurring independently across fields. A broad range of scientific and engineering problems involve multiple scales. Traditional monoscale approaches have proven to be inadequate, even with the largest supercomputers, because of the range of scales and the prohibitively large number of variables involved. Thus, there is a growing need to develop systematic modeling and simulation approaches for multiscale problems. MMS will provide a single broad, authoritative source for results in this area.