This note is concerned with the generalization of the continuous shearlet transform to higher dimensions. Quite recently, a first approach has been derived in [4]. We present an alternative version which deviates from [4] mainly by a different generalization of the shear component. It turns out that the resulting integral transform is again associated with a square-integrable group representation.

For ψ a nontrivial additive character on the finite field Fq, observe that the map t 7→ P x∈Fq ψ(f(x) + tx) is the Fourier transform of the map t 7→ ψ(f(t)). As is well-known, this has a cohomological interpretation, producing a continuous l-adic Galois representation. This paper studies the L-function attached to the k-th symmetric power of this representation using both l-adic and p-adic meth...

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 . . . . . . . . . . . . . . . . . . . . . . . . . ...

Sobolev wavefront sets and 2-microlocal spaces play a key role in describing analyzing the singularities of distributions microlocal analysis solutions partial differential equations. Employing continuous shearlet transform to spaces, this paper we characterize sets, local Hölder distributions/functions. We then establish connections among through transform.

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...

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...

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...

We develop a mathematically-motivated algorithm for image superresolution, based on the discrete shearlet transform. The shearlet transform is strongly directional, and is known to provide nearoptimally sparse representations for a broad class of images. This often leads to superior performance in edge detection and image representation, when compared to other isotropic frames. We justify the u...