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...

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...

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.

in this paper, we give a necessary condition for function in l^2with its dual to generate a dual shearlet tight frame with respect to admissibility.

The shearlet representation has gained increasing recognition in recent years as a framework for the efficient representation of multidimensional data. This representation consists of a countable collection of functions defined at various locations, scales and orientations, where the orientations are obtained through the use of shearing matrices. While shearing matrices offer the advantage of p...

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...