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Proceedings Paper

Design of a tight frame of 2D shearlets based on a fast non-iterative analysis and synthesis algorithm
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Paper Abstract

The shearlet transform is a recent sibling in the family of geometric image representations that provides a traditional multiresolution analysis combined with a multidirectional analysis. In this paper, we present a fast DFT-based analysis and synthesis scheme for the 2D discrete shearlet transform. Our scheme conforms to the continuous shearlet theory to high extent, provides perfect numerical reconstruction (up to floating point rounding errors) in a non-iterative scheme and is highly suitable for parallel implementation (e.g. FPGA, GPU). We show that our discrete shearlet representation is also a tight frame and the redundancy factor of the transform is around 2.6, independent of the number of analysis directions. Experimental denoising results indicate that the transform performs the same or even better than several related multiresolution transforms, while having a significantly lower redundancy factor.

Paper Details

Date Published: 27 September 2011
PDF: 13 pages
Proc. SPIE 8138, Wavelets and Sparsity XIV, 81381Q (27 September 2011); doi: 10.1117/12.893752
Show Author Affiliations
Bart Goossens, Ghent Univ. (Belgium)
Jan Aelterman, Ghent Univ. (Belgium)
Hiêp Luong, Ghent Univ. (Belgium)
Aleksandra Pižurica, Ghent Univ. (Belgium)
Wilfried Philips, Ghent Univ. (Belgium)

Published in SPIE Proceedings Vol. 8138:
Wavelets and Sparsity XIV
Manos Papadakis; Dimitri Van De Ville; Vivek K. Goyal, Editor(s)

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