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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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Shearlet Smoothness Spaces [PDF]
Journal of Fourier Analysis and Applications, 2013 The shearlet representation has gained increasingly more prominence in recent years as a flexible and efficient mathematical framework for the analysis of anisotropic phenomena. This is achieved by combining traditional multiscale analysis with a superior ability to handle directional information.
Lucia Mantovani +2 more
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Iterative CT reconstruction using shearlet-based regularization [PDF]
, 2012 In computerized tomography, it is important to reduce the image noise without increasing the acquisition dose. Extensive research has been done into total variation minimization for image denoising and sparse-view reconstruction. However, TV minimization
Goossens, Bart +6 more
core +1 more source
Multivariate Shearlet Transform, Shearlet Coorbit Spaces and Their Structural Properties [PDF]
, 2012 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 ...
Stephan Dahlke +2 more
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A Multiresolution Image Completion Algorithm for Compressing Digital Color Images
Journal of Applied Mathematics, 2014 This paper introduces a new framework for image coding that uses image inpainting method. In the proposed algorithm, the input image is subjected to image analysis to remove some of the portions purposefully.
R. Gomathi, A. Vincent Antony Kumar
doaj +1 more source
Wavelet/shearlet hybridized neural networks for biomedical image restoration [PDF]
, 2019 Recently, new programming paradigms have emerged that combine parallelism and numerical computations with algorithmic differentiation. This approach allows for the hybridization of neural network techniques for inverse imaging problems with more ...
Burger +12 more
core +1 more source
Recent Progress in Shearlet Theory: Systematic Construction of Shearlet Dilation Groups, Characterization of Wavefront Sets, and New Embeddings [PDF]
Frames and Other Bases in Abstract and Function Spaces, Appl.
Numer. Harmon. Anal., 127-160, 2017, 2016 The class of generalized shearlet dilation groups has recently been developed to allow the unified treatment of various shearlet groups and associated shearlet transforms that had previously been studied on a case-by-case basis. We consider several aspects of these groups: First, their systematic construction from associative algebras, secondly, their ...
arxiv +1 more source
Cone-Adapted Shearlets and Radon Transforms [PDF]
, 2020 19 pages, 3 ...
Bartolucci F., De Mari F., De Vito E.
openaire +4 more sources
, 2012 Anisotropic decompositions using representation systems based on parabolic scaling such as curvelets or shearlets have recently attracted significantly increased attention due to the fact that they were shown to provide optimally sparse approximations of
Grohs, Philipp, Kutyniok, Gitta
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International Journal of Imaging Systems and Technology, Volume 35, Issue 2, March 2025.ABSTRACT Low‐dose computed tomography (CT) images are prone to noise and artifacts caused by photon starvation and electronic noise. Recently, researchers have explored the use of transformer‐based neural networks combined with generative diffusion models, showing promising results in denoising CT images.
Farzan Niknejad Mazandarani +2 more
wiley +1 more source