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

Bart Goossens; Jan Aelterman; Hiêp Luong; Aleksandra Pižurica; Wilfried Philips

doi:10.1117/12.893752

27 September 2011 Design of a tight frame of 2D shearlets based on a fast non-iterative analysis and synthesis algorithm

Bart Goossens, Jan Aelterman, Hiêp Luong, Aleksandra Pižurica, Wilfried Philips

Author Affiliations +

Proceedings Volume 8138, Wavelets and Sparsity XIV; 81381Q (2011) https://doi.org/10.1117/12.893752
Event: SPIE Optical Engineering + Applications, 2011, San Diego, California, United States

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.

Citation Download Citation

Bart Goossens, Jan Aelterman, Hiêp Luong, Aleksandra Pižurica, and Wilfried Philips "Design of a tight frame of 2D shearlets based on a fast non-iterative analysis and synthesis algorithm", Proc. SPIE 8138, Wavelets and Sparsity XIV, 81381Q (27 September 2011); https://doi.org/10.1117/12.893752

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