On The Continuous Steering Of The Scale Of Tight Wavelet Frames

Keywords

Fourier multipliers; Scalability; Tight wavelet frames; Transformability

Abstract

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.

Publication Date

7-21-2016

Publication Title

SIAM Journal on Imaging Sciences

Volume

9

Issue

3

Number of Pages

1042-1062

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1137/15M1033885

Socpus ID

84989339682 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84989339682

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