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...

This paper presents a novel remote sensing image fusion algorithm, which implements panchromatic sharpening of multispectral data through application of the principal component analysis (PCA) transform and the dual-tree compactly supported shearlet transform (DT CSST). Shearlet transforms provide near optimal representation of the anisotropic features of an image. The compactly supported shearl...

In this paper, we introduce pyramid-adapted shearlet systems for the three-dimensional setting, and show how one can construct frames for L(R) with this particular shearlet structure. We then introduce a generalized three-dimensional cartoon-like image model class of piecewise C smooth functions with discontinuities on a C smooth surface with 1 < α ≤ 2 and show that pyramid-adapted shearlet sys...

Shearlet theory has become a central tool in analyzing and representing 2D data with anisotropic features. Shearlet systems are systems of functions generated by one single generator with parabolic scaling, shearing, and translation operators applied to it, in much the same way wavelet systems are dyadic scalings and translations of a single function, but including a precise control of directio...

This papers examines structural properties of the recently developed shearlet coorbit spaces in higher dimensions. We prove embedding theorems for subspaces of shearlet coorbit spaces resembling shearlets on the cone in three dimensions into Besov spaces. The results are based on general atomic decompositions of Besov spaces. Furthermore, we establish trace results for these subspaces with resp...

    Necessary conditions for  shearlet  and cone-adapted shearlet systems to be frames are presented with respect to the admissibility condition of generators.

In this paper, a new bivariate shrinkage denoising method is proposed to model statistics of shearlet coefficients of images. Using Bayesian estimation theory we derive from this model a simple non-linear shrinkage function for shearlet denoising, which generalizes the soft threshold approach. Experimental results show that the proposed method can remove Gaussian white noise while effectively p...

This chapter is devoted to the generalization of the continuous shearlet transform to higher dimensions as well as to the construction of associated smoothness spaces and to the analysis of their structural properties, respectively. To construct canonical scales of smoothness spaces , so-called shearlet coorbit spaces , and associated atomic decompositions and Banach frames we prove that the ge...

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...

We prove a Heisenberg type uncertainty principle for the continuous shearlet transform, and study two generalizations of it. Our work extends the shearlet theory. c ©2016 All rights reserved.