Development of a digital shearlet transform based on Pseudo-Polar FFT

Gitta Kutyniok; Morteza Shahram; David L. Donoho

doi:10.1117/12.825656

4 September 2009 Development of a digital shearlet transform based on Pseudo-Polar FFT

Gitta Kutyniok, Morteza Shahram, David L. Donoho

Proceedings Volume 7446, Wavelets XIII; 74460B (2009) https://doi.org/10.1117/12.825656
Event: SPIE Optical Engineering + Applications, 2009, San Diego, California, United States

Abstract

Shearlab is a Matlab toolbox for digital shearlet transformation of two-D (image) data we developed following a rational design process. The Pseudo-Polar FFT fits very naturally with the continuum theory of the Shearlet transform and allows us to translate Shearlet ideas naturally into a digital framework. However, there are still windows and weights which must be chosen. We developed more than a dozen performance measures quantifying precision of the reconstruction, tightness of the frame, directional and spatial localization and other properties. Such quantitative performance metrics allow us to: (a) tune parameters and objectively improve our implementation; and (b) compare different directional transform implementations. We present and interpret the most important performance measures for our current implementation.

Citation Download Citation

Gitta Kutyniok, Morteza Shahram, and David L. Donoho "Development of a digital shearlet transform based on Pseudo-Polar FFT", Proc. SPIE 7446, Wavelets XIII, 74460B (4 September 2009); https://doi.org/10.1117/12.825656

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