27 September 2011 Efficient multiscale and multidirectional representation of 3D data using the 3D discrete shearlet transform
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Abstract
In recent years, there has been a lot of interest in multiresolution representations that also perform a multidirectional analysis. These representations often yield very sparse representation for multidimensional data. The shearlet representation, which has been derived within the framework of composite wavelets, can be extended quite trivially from 2D to 3D. However, the extension to 3D is not unique and consequently there are different implementations possible for the discrete transform. In this paper, we investigate the properties of two relevant designs having different 3D frequency tilings. We show that the first design has a redundancy factor of around 7, while in the second design the transform can attain a redundancy factor around 3.5, independent of the number of analysis directions. Due to the low redundancy, the 3D shearlet transform becomes a viable alternative to the 3D curvelet transform. Experimental results are provided to support these findings.
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Bart Goossens, Hiêp Luong, Jan Aelterman, Aleksandra Pižurica, Wilfried Philips, "Efficient multiscale and multidirectional representation of 3D data using the 3D discrete shearlet transform", Proc. SPIE 8138, Wavelets and Sparsity XIV, 81381Z (27 September 2011); doi: 10.1117/12.893808; https://doi.org/10.1117/12.893808
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