We introduced the continuous and discrete $p$-adic shearlet systems. We restrict ourselves to a brief description of the $p$-adic theory and shearlets in real case. Using the group $G_p$ consist of all $p$-adic numbers that all of its elements have a square root, we defined the continuous $p$-adic shearlet system associated with $L^2left(Q_p^{2}right)$. The discrete $p$-adic shearlet frames for...

This report provides an expository summary of the proof of optimal shearlet approximation (compact support case). We only discuss the non-smooth part of the approximation. For further details, the readers are referred to [1], [2] and the references therein. I. COMPACTLY SUPPORTED SHEARLET FRAME A. Some Notations • parabolic scaling matrices: A2j = 2j 0 0 2  or Ã2j = 2j/2 0 0 2  , for j ...

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...

We propose an algorithmic framework based on ADMM/split Bregman that combines a multilevel adapted, iterative reweighting strategy and a second total generalized variation regularizer. The level adapted reweighting strategy is a combination of reweighted `-minimization and additional compensation factors for a uniform treatment of the sparsity structure across all levels. Classical multilscale ...

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...

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...

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...