Gabor Shearlets

TL;DR

This paper introduces Gabor shearlets, a novel shearlet variant combining Gabor and wavelet frames, enabling low-redundancy, sparse approximations of cartoon-like functions with standard filters.

Contribution

The paper presents a new Gabor shearlet system that achieves near-minimal redundancy and can be implemented with standard wavelet and Gabor filters, extending shearlet theory.

Findings

Achieves redundancy close to one.

Provides tight frame with Meyer filters.

Effective sparse approximation of cartoon-like functions.

Abstract

In this paper, we introduce Gabor shearlets, a variant of shearlet systems, which are based on a different group representation than previous shearlet constructions: they combine elements from Gabor and wavelet frames in their construction. As a consequence, they can be implemented with standard filters from wavelet theory in combination with standard Gabor windows. Unlike the usual shearlets, the new construction can achieve a redundancy as close to one as desired. Our construction follows the general strategy for shearlets. First we define group-based Gabor shearlets and then modify them to a cone-adapted version. In combination with Meyer filters, the cone-adapted Gabor shearlets constitute a tight frame and provide low-redundancy sparse approximations of the common model class of anisotropic features which are cartoon-like functions.