Gabor shearlets (Q466975)

In this paper, the authors introduce new Gabor shearlets based on a group related to chirp modulations and discuss their frame properties and the associated multiresolution structure. The Gabor shearlets form a unit-norm \(b^{-1}\)-tight frame for \(L^2({\mathbb R}^2)\), where \(b^{-1}\) can be chosen close to 1. Gabor shearlets can achieve a redundancy as close to 1 as desired. Further, the Gabor shearlets have polynomial decay in \({\mathbb R}^2\).NEWLINENEWLINEThen cone-adapted Gabor shearlets are defined by a projection of Gabor shearlets on cones in the frequency domain. The authors show that cone-adapted Gabor shearlets provide optimally sparse approximations of cartoon-like functions.