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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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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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Mathematische Nachrichten, 2022 AbstractWe develop a distributional framework for the shearlet transform and the shearlet synthesis operator , where is the Lizorkin test function space and is the space of highly localized test functions on the standard shearlet group . These spaces and their duals are called Lizorkin type spaces of test functions and distributions.
Francesca Bartolucci +2 more
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Uncertainty Principles For The Continuous Quaternion Shearlet Transform
Advances in Applied Clifford Algebras, 2019In this paper, authors have studied some novel uncertainty principles for the continuous quaternion shearlet transform using the machinery of quaternion convolution, quaternion Fourier transform and operator theory. Besides, the fundamental properties including the Parseval's and reconstruction formulae, the Heisenberg-type uncertainty principles are ...
Kamel Brahim, Bochra Nefzi
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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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3-D Discrete Shearlet Transform and Video Processing
IEEE Transactions on Image Processing, 2012In this paper, we introduce a digital implementation of the 3-D shearlet transform and illustrate its application to problems of video denoising and enhancement. The shearlet representation is a multiscale pyramid of well-localized waveforms defined at various locations and orientations, which was introduced to overcome the limitations of traditional ...
Pooran Singh Negi, Demetrio Labate
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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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