In this paper, we focus on the study of shearlet transform which isdened by using the hyperbolic functions. As a result we check an admissibilitycondition such that implies the reconstruction formula. To this end, we will usethe concept of the classical shearlet, which indicates the position and directionof a singularity.

The field $Q_{p}$ of $p$-adic numbers is defined as the completion of the field of the rational numbers $Q$ with respect to the  $p$-adic norm $|.|_{p}$. In this paper, we study the continuous and discrete $p-$adic shearlet systems on $L^{2}(Q_{p}^{2})$. We also suggest discrete $p-$adic shearlet frames. Several examples are provided.

With the growth of digital networks such as the Internet, digital media have been explosively developed in e-commerce and online services. This causes problems such as illegal copy and fake ownership. Watermarking is proposed as one of the solutions to such cases. Among different watermarking techniques, the wavelet transform has been used more because of its good ability in modeling the human ...

we regard the shearlet group as a semidirect product group andshow that its standard representation is,typically, a quasiregu-lar representation. as a result we can characterize irreducibleas well as square-integrable subrepresentations of the shearletgroup.

Watermarking is one of the best solutions for copyright protection and authentication of multimedia contents. In this paper a hybrid scheme is proposed using wavelet and shearlet transforms with singular value decomposition. For better security, Arnold map is used for encryption. Examining the results and comparing with other methods show that this hybrid proposed scheme with simultaneous utili...

Over the past years, various representation systems which sparsely approximate functions governed by anisotropic features such as edges in images have been proposed. We exemplarily mention the systems of contourlets, curvelets, and shearlets. Alongside the theoretical development of these systems, algorithmic realizations of the associated transforms were provided. However, one of the most comm...

Recent advances in high-resolution fluorescence microscopy have enabled the systematic study of morphological changes in large populations of cells induced by chemical and genetic perturbations, facilitating the discovery of signaling pathways underlying diseases and the development of new pharmacological treatments. In these studies, though, due to the complexity of the data, quantification an...