Wave atoms and sparsity of oscillatory patterns

被引:206
作者
Demanet, Laurent [1 ]
Ying, Lexing
机构
[1] Stanford Univ, Dept Math, Stanford, CA 94305 USA
[2] Univ Texas, Dept Math, Austin, TX 78712 USA
基金
美国国家科学基金会;
关键词
wave atoms; image processing; texture; oscillatory; warping; diffeomorphism;
D O I
10.1016/j.acha.2007.03.003
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We introduce "wave atoms" as a variant of 2D wavelet packets obeying the parabolic scaling wavelength similar to (diameter)(2). We prove that warped oscillatory functions, a toy model for texture, have a significantly sparser expansion in wave atoms than in other fixed standard representations like wavelets, Gabor atoms, or curvelets. We propose a novel algorithm for a tight frame of wave atoms with redundancy two, directly in the frequency plane, by the "wrapping" technique. We also propose variants of the basic transform for applications in image processing, including an orthonormal basis, and a shift-invariant tight frame with redundancy four. Sparsity and denoising experiments on both seismic and fingerprint images demonstrate the potential of the tool introduced. (c) 2007 Elsevier Inc. All rights reserved.
引用
收藏
页码:368 / 387
页数:20
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