Volumetric data acquisition and increasingly massive data storage have increased the need to develop better analysis tools for three-dimensional data sets. These volumetric data sets can provide information beyond that contained in standard two-dimensional images. Common strategies to deal with such data sets have been based on sequential use of two-dimensional analysis tools. In this work, we ...

To reduce the x-ray dose in computerized tomography (CT), many constrained optimization approaches have been proposed aiming at minimizing a regularizing function that measures lack of consistency with some prior knowledge about the object that is being imaged, subject to a (predetermined) level of consistency with the detected attenuation of x-rays. One commonly investigated regularizing funct...

Shearlet systems have so far been only considered as a means to analyze L2-functions defined on R2, which exhibit curvilinear singularities. However, in applications such as image processing or numerical solvers of partial differential equations the function to be analyzed or efficiently encoded is typically defined on a non-rectangular shaped bounded domain. Motivated by these applications, in...

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...

Under the linear approximation model for error diffusion halftoning, a shearlet-based inverse halftoning (SIH) algorithm is proposed. The SIH algorithm performs inverse halftoning by first inverting the modelspecified convolution operator and then reducing the residual color noise using scalar shearlet-domain thresholding. The optimal thresholds are derived by using the maximum a posteriori rul...

This paper presents a new filtering approach for Synthetic Aperture Radar (SAR) interferometric phase noise reduction in the shearlet domain, depending on the coherent statistical characteristics. Shearlets provide a multidirectional and multiscale decomposition that have advantages over wavelet filtering methods when dealing with noisy phase fringes. Phase noise in SAR interferograms is direct...

In this paper, we focus on the study of shearlet transform which isdened 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.

The field $Q_{p}$ of $p$-adic numbers is defined as the completion of the field of the rational numbers $Q$ with respect to the  $p$-adic norm $|.|_{p}$. In this paper, we study the continuous and discrete $p-$adic shearlet systems on $L^{2}(Q_{p}^{2})$. We also suggest discrete $p-$adic shearlet frames. Several examples are provided.