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Proceedings Paper

Curvelets and wave atoms for mirror-extended images
Author(s): Laurent Demanet; Lexing Ying
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Paper Abstract

We present variants of both the digital curvelet transform, and the digital wave atom transform, which handle the image boundaries by mirror extension. Previous versions of these transforms treated image boundaries by periodization. The main ideas of the modifications are 1) to tile the discrete cosine domain instead of the discrete Fourier domain, and 2) to adequately reorganize the in-tile data. In their shift-invariant versions, the new constructions come with no penalty on the redundancy or computational complexity. For shift-variant wave atoms, the penalty is a factor 2 instead of the naive factor 4. These various modifications have been included in the CurveLab and WaveAtom toolboxes, and extend the range of applicability of curvelets (good for edges and bandlimited wavefronts) and wave atoms (good for oscillatory patterns and textures) to situations where periodization at the boundaries is uncalled for. The new variants are dubbed ME-curvelets and ME-wave atoms, where ME stands for mirror-extended.

Paper Details

Date Published: 20 September 2007
PDF: 14 pages
Proc. SPIE 6701, Wavelets XII, 67010J (20 September 2007); doi: 10.1117/12.733257
Show Author Affiliations
Laurent Demanet, Stanford Univ. (United States)
Lexing Ying, Univ. of Texas at Austin (United States)


Published in SPIE Proceedings Vol. 6701:
Wavelets XII
Dimitri Van De Ville; Vivek K. Goyal; Manos Papadakis, Editor(s)

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