In This paper, we give a necessary condition for function in $L^2$ with its dual to generate a dual shearlet tight frame with respect to admissibility.

This paper first proposes a novel image separation method based on the hyperanalytic shearlet. By combining the advantages of both the hyperanalytic wavelet transform and the shear operation, hyperanalytic shearlet is easy to implement and also has a low redundancy. By using such transform and the orthonormal wavelet, a new geometric separation dictionary is obtained which can sparsely represen...

‎This paper is devoted to definition standard higher dimension shearlet group $ mathbb{S} = mathbb{R}^{+} times mathbb {R}^{n-1} times mathbb {R}^{n} $ and determination of square integrable subrepresentations of this group‎. ‎Also we give a characterisation of admissible vectors associated to the Hilbert spaces corresponding to each su brepresentations‎.

It is a challenging task to reconstruct images from their noisy, blurry, and/or incomplete measurements, especially those with important details and features such as medical magnetic resonance (MR) and CT images. We propose a novel regularization model that integrates two recently developed regularization tools: total generalized variation (TGV) by Bredies, Kunisch, and Pock; and shearlet trans...