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The continuous shearlet transform in arbitrary dimensions
, 2008 Dahlke, Stephan +2 more
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Continuous Modulated Shearlet Transform
Advances in Pure and Applied Mathematics, 2022Summary: We generalize the well-known transforms such as short-time Fourier transform, wavelet transform and shearlet transform and refer it as Continuous Modulated Shearlet Transform. Important properties like Plancherel formula and inversion formula have been investigated. Uncertainty inequalities associated with this transform are presented.
Bansal, Piyush +2 more
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The Discrete Shearlet Transform: A New Directional Transform and Compactly Supported Shearlet Frames
IEEE Transactions on Image Processing, 2010It is now widely acknowledged that analyzing the intrinsic geometrical features of the underlying image is essential in many applications including image processing. In order to achieve this, several directional image representation schemes have been proposed.
Wang-Q Lim
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Abstract Shearlet Transform [PDF]
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2015 Approximately ten years ago the generalization of wavelets to shearlets started its development. This paper extends shearlets (introduced in 2005 to find efficient extensions for the classical wavelet transform, see among others \textit{G. Kutyniok} and \textit{D. Labate} [``Construction of regular and irregular shearlet frames'', J.
Kamyabi-Gol, R.A., Atayi, V.
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Clifford Valued Shearlet Transform
Advances in Applied Clifford Algebras, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sharma, Jyoti, Singh, Shivam Kumar
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SHEARLET TRANSFORMS AND DIRECTIONAL REGULARITIES
International Journal of Wavelets, Multiresolution and Information Processing, 2010In an effort to characterize uniform and pointwise Hölder regularities, we obtain necessary decay rates and sufficient decay rates of continuous and discrete shearlet transform across scales. They are the same rates as those of the Hart Smith and continuous curvelet transforms.
P. Lakhonchai +2 more
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Shearlets as Multi-scale Radon Transforms
Sampling Theory in Signal and Image Processing, 2017It is shown that the 2D-shearlet transform is the composition of the affine Radon transform, a 1D-wavelet transform and a 1D-convolution. This is applied to give an alternative proof of the fact that the shearlet transform is able to resolve the wavefront set associated with the unit disc.
BARTOLUCCI, FRANCESCA +3 more
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COORBIT SPACE THEORY FOR THE TOEPLITZ SHEARLET TRANSFORM
International Journal of Wavelets, Multiresolution and Information Processing, 2012In 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.
Stephan Dahlke +2 more
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THE UNCERTAINTY PRINCIPLE ASSOCIATED WITH THE CONTINUOUS SHEARLET TRANSFORM
International Journal of Wavelets, Multiresolution and Information Processing, 2008Finding optimal representations of signals in higher dimensions, in particular directional representations, is currently the subject of intensive research. Since the classical wavelet transform does not provide precise directional information in the sense of resolving the wavefront set, several new representation systems were proposed in the past ...
Stephan Dahlke +5 more
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On the shearlet transform using hyperbolic functions
2014Summary: In this paper, we focus on the study of shearlet transform which is defined by using the hyperbolic functions. As a result, we check an admissibility condition such that implies the reconstruction formula. To this end, we use the concept of the classical shearlet, which indicates the position and direction of a singularity.
Zare, Masoumeh +2 more
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