Necessary conditions for  shearlet  and cone-adapted shearlet systems to be frames are presented with respect to the admissibility condition of generators.

In this paper, a new bivariate shrinkage denoising method is proposed to model statistics of shearlet coefficients of images. Using Bayesian estimation theory we derive from this model a simple non-linear shrinkage function for shearlet denoising, which generalizes the soft threshold approach. Experimental results show that the proposed method can remove Gaussian white noise while effectively p...

This chapter is devoted to the generalization of the continuous shearlet transform to higher dimensions as well as to the construction of associated smoothness spaces and to the analysis of their structural properties, respectively. To construct canonical scales of smoothness spaces , so-called shearlet coorbit spaces , and associated atomic decompositions and Banach frames we prove that the ge...

Abstract. Multivariate problems are typically governed by anisotropic features such as edges in images. A common bracket of most of the various directional representation systems which have been proposed to deliver sparse approximations of such features is the utilization of parabolic scaling. One prominent example is the shearlet system. Our objective in this paper is three-fold: We firstly de...

We prove a Heisenberg type uncertainty principle for the continuous shearlet transform, and study two generalizations of it. Our work extends the shearlet theory. c ©2016 All rights reserved.

in this paper, we give a necessary condition for function in l^2with its dual to generate a dual shearlet tight frame with respect to admissibility.

The two-dimensional wavelet transform for magnetic resonance imaging (MRI) images does not sparsely represent curve singularity characteristics, which can only capture the limited direction information. Pointing at this problem, this paper presents a new method based on discrete Shearlet transform for compressed sensing MRI (CS-MRI). Frequency coefficients can be got at all scales and in all di...

This paper introduces a numerical implementation of the 3D shearlet transform, a directional transform which is derived from the theory of shearlets. The shearlet approach belongs to a class of directional multiscale methods emerged during the last 10 years to overcome the limitations of traditional multiscale systems, which also include curvelets and contourlets. Unlike other methods, shearlet...

The two-dimensional wavelet transform for magnetic resonance imaging (MRI) does not represent sparsely curve singularity characteristics, it can only capture the limited direction information. In order to solve this problem, a new method for compressed sensing MRI (CS-MRI) is presented based on discrete shearlet transform in this paper. Frequency coefficients can be got at all scales and in all...

Medical image fusion is a technique that integrates complementary information from multimodality images. The fused image is more suitable for treatment plan strategies. In this paper, an efficient medical image fusion method has been proposed based on shearlet transform and human visibility feature as fusion rule. Image fusion rule is the solution that influences the quality of image fusion. Th...