In this paper we provide a construction of multiscale systems on a bounded domain Ω ⊂ R coined boundary shearlet systems, which satisfy several properties advantageous for applications to imaging science and numerical analysis of partial differential equations. More precisely, we construct a boundary shearlet system that forms a frame for L(Ω) with controllable frame bounds and admits optimally...

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...

Despite the growing growth of technology, handwritten signature has been selected as the first option between biometrics by users. In this paper, a new methodology for offline handwritten signature verification and recognition based on the Shearlet transform and transfer learning is proposed. Since, a large percentage of handwritten signatures are composed of curves and the performance of a sig...

The inversion of the Radon transform is a classical ill-posed inverse problem where some method of regularization must be applied in order to accurately recover the objects of interest from the observable data. A well-known consequence of the traditional regularization methods is that some important features to be recovered are lost, as evident in imaging applications where the regularized reco...

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

Abstract. We study efficient and reliable methods of capturing and sparsely representing anisotropic structures in 3D data. As a model class for multidimensional data with anisotropic features, we introduce generalized three-dimensional cartoon-like images. This function class will have two smoothness parameters: one parameter β controlling classical smoothness and one parameter α controlling a...

In this paper, we first introduce the concept of an adaptive MRA (AMRA) structure which is a variant of the classical MRA structure suited to the main goal of a fast flexible decomposition strategy adapted to the data at each decomposition level. We then study this novel methodology for the general case of affine-like systems, and derive a Unitary Extension Principle (UEP) for filter design. Fi...

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...

Recently introduced inpainting algorithms using a combination of applied harmonic analysis and compressed sensing have turned out to be very successful. One key ingredient is a carefully chosen representation system which provides (optimally) sparse approximations of the original image. Due to the common assumption that images are typically governed by anisotropic features, directional represen...