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 study the construction of irregular shearlet systems, i.e., systems of the form SH(ψ,Λ) = {a− 4 ψ(A−1 a S−1 s (x− t)) : (a, s, t) ∈ Λ}, where ψ ∈ L(R), Λ is an arbitrary sequence in R ×R×R2, Aa is a parabolic scaling matrix and Ss a shear matrix. These systems are obtained by appropriately sampling the Continuous Shearlet Transform. We derive sufficient conditions for such a d...

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...

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.

The present paper for the first time constructs a frame/dual frame pair of shearlet type such that both frames possess the distinctive time-frequency localization properties needed in establishing their desirable approximation properties. Our construction is based on a careful pasting together of two bandlimited shearlet Parseval frames associated with two different frequency cones, inspired by...

Shearlab is a Matlab toolbox for digital shearlet transformation of two-D (image) data we developed following a rational design process. The Pseudo-Polar FFT fits very naturally with the continuum theory of the Shearlet transform and allows us to translate Shearlet ideas naturally into a digital framework. However, there are still windows and weights which must be chosen. We developed more than...

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...