On The Continuous Steering of the Scale of Tight Wavelet Frames
This work provides a method for enhancing wavelet-based signal processing, particularly in applications requiring adjustable frequency bands, but it appears incremental as it builds on existing steerable wavelet concepts.
The paper tackles the problem of creating adaptable tight wavelet frames with controllable scaling, analogous to steerable wavelets, by using Fourier multipliers that can be scaled via matrix multiplication. The result is improved frequency localization with efficient scaling operations.
In analogy with steerable wavelets, we 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. 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 improve the frequency localization. Importantly, the localized frequency bands specified by this construction can be scaled efficiently using matrix multiplication.