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.

‎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.

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.

Recently, shearlet groups have received much attention in connection with shearlet transforms applied for orientation sensitive image analysis and restoration. The square integrable representations of the shearlet groups provide not only the basis for the shearlet transforms but also for a very natural definition of scales of smoothness spaces, called shearlet coorbit spaces. The aim of this pa...

In this paper, we present a new image denoising method for removing Gaussian noise from corrupted image by using shearlet transform and nonlinear diffusion. The image is decomposed by the shearlet transform to obtain the shearlet coefficients in each subband; then a diffusion scheme based on statistical property of shearlet coefficients is used to shrink noisy shearlet coefficients. The test sh...

In this paper, we first develop a digital shearlet theory which is rationally designed in the sense that it is the digitalization of the existing shearlet theory for continuum data. This shows that shearlet theory indeed provides a unified treatment for the continuum and digital realm. Secondly, we discuss our implementation of the associated digital shearlet transform. This software package ca...

The shearlet representation has gained increasingly more prominence in recent years as a flexible mathematical framework which enables the efficient analysis of anisotropic phenomena by combining multiscale analysis with the ability to handle directional information. In this paper, we introduce a class of shearlet smoothness spaces which is derived from the theory of decomposition spaces recent...

Shearlet as a new multidirectional and multiscale transform is optimally efficient in representing images containing edges. In this paper, a total variation based multivariate shearlet adaptive shrinkage is proposed for discontinuity-preserving image denoising. The multivariate adaptive threshold is employed to reduce the noise. Projected total variation diffusion is used to suppress the pseudo...

in this paper, we focus on the study of shearlet transform which isdened 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.

3 Computation of the shearlet transform 13 3.1 Finite discrete shearlets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.2 A discrete shearlet frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.3 Inversion of the shearlet transform . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.4 Smooth shearlets . . . . . . . . . . . . . . . . . . . . . . . . . ...