Scaling Families of Fourier Multipliers and Tight Wavelet Frames
Zsuzsanna Püspöki, LIB | STI | EPFL

Seminar • 02 March 2015 • BIG 4.235

Abstract
In analogy with steerable wavelets, I will present a general construction of adaptable tight wavelet frames, with an emphasis on scaling operations. In particular, the derived wavelets can be “dilated” by a procedure comparable to the operation of steering steerable wavelets. Furthermore, the fundamental aspects of the construction are the same; an admissible collection of Fourier multipliers is used to extend a tight wavelet frame, and the “scale” of the wavelets is adapted by scaling the multipliers. As an application, the proposed wavelets can be used to provide increased frequency localization, and importantly, the localized frequency bands specified by this construction can be efficiently adapted using matrix multiplication. Numerical experiments are presented to justify the method, and I also present results for feature extraction from real data.