In this paper, using shearlet frames, we present a numerical  method  for solving  the wave equation. We define a new shearlet system and by the Plancherel theorem, we calculate the shearlet coefficients.

The selection of features extracted for image retrieval is quite important. We in this paper choose standard deviation and kurtosis to character texture. Non-subsampled shearlet transform is used to derive texture features. Shearlet is a new sparse representation tool of multidimensional function, which provides a simple and efficient mathematical framework. We firstly decompose the source imag...

In this paper we are concerned with the continuous shearlet transform in arbitrary space dimensions where the shear operation is of Toeplitz type. In particular, we focus on the construction of associated shearlet coorbit spaces and on atomic decompositions and Banach frames for these spaces.

In this paper we will study the Continuous Shearlet Transform from a wavelet point of view, and show how this perspective can be used to derive a new geometric interpretation of this transform providing the possibility for FFT-based fast methods to compute the Continuous Shearlet Transform.

We analyze the detection and classification of singularities of functions f = χB , where B ⊂ R and d = 2, 3. It will be shown how the set ∂B can be extracted by a continuous shearlet transform associated with compactly supported shearlets. Furthermore, if ∂S is a d−1 dimensional piecewise smooth manifold with d = 2 or 3, we will classify smooth and non-smooth components of ∂S. This improves pre...

This note is concerned with the generalization of the continuous shearlet transform to higher dimensions. Similar to the twodimensional case, our approach is based on translations, anisotropic dilations and specific shear matrices. We show that the associated integral transform again originates from a square-integrable representation of a specific group, the full n-variate shearlet group. Moreo...

This paper presents a novel remote sensing image fusion algorithm, which implements the intensity-hue-saturation (IHS) transform on panchromatic sharpening of multispectral data and the dual-tree compactly supported shearlet transform (DT CSST) during fusion. Shearlet transforms can provide almost optimal representation of the anisotropic features of an image. The spatial domain discrete implem...

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...

The continuous curvelet and shearlet transforms have recently been shown to be much more effective than the traditional wavelet transform in dealing with the set of discontinuities of functions and distributions. In particular, the continuous shearlet transform has the ability to provide a very precise geometrical characterization of general discontinuity curves occurring in images. In this pap...