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, Hiep Quang Luong, Aleksandra Pižurica, Wilfried R. Philips · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2013
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.