A split-augmented Lagrangian algorithm for spectral factorization of a set of 2D directional filters and application to the design of compact shearlet frames

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

doi:10.1117/12.2024876

26 September 2013 A split-augmented Lagrangian algorithm for spectral factorization of a set of 2D directional filters and application to the design of compact shearlet frames

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

Author Affiliations +

Proceedings Volume 8858, Wavelets and Sparsity XV; 885806 (2013) https://doi.org/10.1117/12.2024876
Event: SPIE Optical Engineering + Applications, 2013, San Diego, California, United States

Abstract

In this paper, we first briefly review the directional properties of the Dual-Tree complex wavelet transform and we investigate how the directional selectivity of the transform can be increased (i.e., to obtain more than 6 orientations per scale). To this end, we describe a new augmented Lagrangian optimization algorithm to jointly perform the 2D spectral factorization of a set of 2D directional filters, with a high numerical accuracy. We demonstrate how this approach can be used to design compactly supported shearlet frames that are tight. Finally, a number of experimental results are given to show the merits of the resulting shearlet frames.

Citation Download Citation

Bart Goossens, Jan Aelterman, Hiêp Luong, Aleksandra Pižurica, and Wilfried Philips "A split-augmented Lagrangian algorithm for spectral factorization of a set of 2D directional filters and application to the design of compact shearlet frames", Proc. SPIE 8858, Wavelets and Sparsity XV, 885806 (26 September 2013); https://doi.org/10.1117/12.2024876

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