The Continuous Shearlet Transform in Arbitrary Space Dimensions, Frame Construction, and Analysis of Singularities
نویسندگان
چکیده
This note is concerned with the generalization of the continuous shearlet transform to higher dimensions. Similar to the two-dimensional 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. Moreover, we verify that by applying the coorbit theory, canonical scales of smoothness spaces and associated Banach frames can be derived. We also indicate how our transform can be used to characterize singularities in signals.
منابع مشابه
The Continuous Shearlet Transform in Arbitrary Space Dimensions
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...
متن کاملCoorbit Space Theory for the Toeplitz Shearlet Transform
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.
متن کاملMultivariate Shearlet Transform, Shearlet Coorbit Spaces and their Structural Properties
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...
متن کاملرفع نوفه ویدئو توسط تبدیل قیچک قطعهای
Parabolic scaling and anisotropic dilation form the core of famous multi-resolution transformations such as curvelet and shearlet, which are widely used in signal processing applications like denoising. These non-adaptive geometrical wavelets are commonly used to extract structures and geometrical features of multi-dimensional signals and preserve them in noise removal treatments. In discrete s...
متن کاملConstruction of Regular and Irregular Shearlet Frames
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...
متن کامل