Critically Sampled Wavelets With Composite Dilations

Glenn R. Easley

doi:10.1109/TIP.2011.2164415

Return

Critically Sampled Wavelets With Composite Dilations

2012-02-01

PRE

Glenn R. Easley *

Demetrio Labate

DOI：10.1109/TIP.2011.2164415

Original

Original request for help

Save

Abstract

En 中文

Wavelets with composite dilations provide a general framework for the construction of waveforms defined not only at various scales and locations, as traditional wavelets, but also at various orientations and with different scaling factors in each coordinate. As a result, they are useful to analyze the geometric information that often dominate multidimensional data much more efficiently than traditional wavelets. The shearlet system, for example, is a particular well-known realization of this framework, which provides optimally sparse representations of images with edges. In this paper, we further investigate the constructions derived from this approach to develop critically sampled wavelets with composite dilations for the purpose of image coding. Not only do we show that many nonredundant directional constructions recently introduced in the literature can be derived within this setting, but we also introduce new critically sampled discrete transforms that achieve much better nonlinear approximation rates than traditional discrete wavelet transforms and outperform the other critically sampled multiscale transforms recently proposed.

Keywords:

Contourlets

directional filter banks

image coding

nonlinear approximations (NLAs)

shearlets

wavelets

AI Summary

Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.