Shearlets: from theory to deep learning

DOI10.1007/978-3-030-98661-2_80zbMath1547.94045MaRDI QIDQ6606472

Gitta Kutyniok

Publication date: 16 September 2024

zbMATH Keywords

waveletsframessparse approximationshearletsdeep neural networks

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Artificial neural networks and deep learning (68T07) Learning and adaptive systems in artificial intelligence (68T05) Computing methodologies for image processing (68U10) Numerical methods for wavelets (65T60) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) General harmonic expansions, frames (42C15)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(\alpha\)-Molecules
• Parabolic molecules
• Shearlet smoothness spaces
• Cartoon approximation with \(\alpha\)-curvelets
• Classification of edges using compactly supported shearlets
• Irregular shearlet frames: Geometry and approximation properties
• Compactly supported shearlets are optimally sparse
• Continuous shearlet frames and resolution of the wavefront set
• Shearlet coorbit spaces: Compactly supported analyzing shearlets, traces and embeddings
• Construction of compactly supported shearlet frames
• Continuous shearlet tight frames
• Shearlet coorbit spaces and associated Banach frames
• Sparse directional image representations using the discrete shearlet transform
• The continuous shearlet transform in arbitrary space dimensions
• Edge analysis and identification using the continuous shearlet transform
• The analysis of linear partial differential operators. I: Distribution theory and Fourier analysis.
• Bendlets: a second-order shearlet transform with bent elements
• Image analysis with two-dimensional continuous wavelet transform
• Shearlet coorbit spaces: traces and embeddings in higher dimensions
• Bandlimited shearlet-type frames with nice duals
• Analysis of inpainting via clustered sparsity and microlocal analysis
• Geometric separation by single-pass alternating thresholding
• Smooth projections and the construction of smooth Parseval frames of shearlets
• The Mathematics of Computerized Tomography
• ShearLab 3D
• Convex multiclass segmentation with shearlet regularization
• Clustered Sparsity and Separation of Cartoon and Texture
• Introduction to Shearlets
• Image Processing Using Shearlets
• Image Separation Using Wavelets and Shearlets
• Singularities of the X-Ray Transform and Limited Data Tomography in $\mathbb{R}^2 $ and $\mathbb{R}^3 $
• Optimally Sparse Approximations of 3D Functions by Compactly Supported Shearlet Frames
• THE UNCERTAINTY PRINCIPLE ASSOCIATED WITH THE CONTINUOUS SHEARLET TRANSFORM
• Resolution of the wavefront set using continuous shearlets
• Ten Lectures on Wavelets
• New tight frames of curvelets and optimal representations of objects with piecewise C² singularities
• Solving ill-posed inverse problems using iterative deep neural networks
• Deep Convolutional Neural Network for Inverse Problems in Imaging
• An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
• Optimal Compressive Imaging of Fourier Data
• Microlocal Analysis of the Geometric Separation Problem
• The Construction of Smooth Parseval Frames of Shearlets
• Introduction to Finite Frame Theory
• Extraction of Digital Wavefront Sets Using Applied Harmonic Analysis and Deep Neural Networks
• Shearlets as feature extractor for semantic edge detection: the model-based and data-driven realm
• Asymptotic Analysis of Inpainting via Universal Shearlet Systems
• A Shearlet Approach to Edge Analysis and Detection
• The Discrete Shearlet Transform: A New Directional Transform and Compactly Supported Shearlet Frames
• Nonseparable Shearlet Transform
• Learning the invisible: a hybrid deep learning-shearlet framework for limited angle computed tomography
• Optimally Sparse Multidimensional Representation Using Shearlets
• Sparse Image and Signal Processing
• An introduction to frames and Riesz bases
• Sparse components of images and optimal atomic decompositions

This page was built for publication: Shearlets: from theory to deep learning