NESTANets: stable, accurate and efficient neural networks for analysis-sparse inverse problems

DOI10.1007/s43670-022-00043-5OpenAlexW4313437003MaRDI QIDQ2700171

Ben Adcock, Maksym Neyra-Nesterenko

Publication date: 20 April 2023

Published in: Sampling Theory, Signal Processing, and Data Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.00804

zbMATH Keywords

inverse problemsdeep learningunrollingadversarial perturbationsNESTArestart scheme

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Artificial neural networks and deep learning (68T07) Convex programming (90C25) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Inverse problems in linear algebra (15A29)

Uses Software

• NESTA
• PyTorch
• MRI Simulation and Reconstruction

Cites Work

• Unnamed Item
• Unnamed Item
• Smooth minimization of non-smooth functions
• On the ergodic convergence rates of a first-order primal-dual algorithm
• Compactly supported shearlets are optimally sparse
• Parseval proximal neural networks
• The cosparse analysis model and algorithms
• Recovering edges in ill-posed inverse problems: Optimality of curvelet frames.
• A first-order primal-dual algorithm for convex problems with applications to imaging
• A review on deep learning in medical image reconstruction
• Stability and robustness of \(\ell_1\)-minimizations with Weibull matrices and redundant dictionaries
• \(\ell^1\)-analysis minimization and generalized (co-)sparsity: when does recovery succeed?
• A simple nearly optimal restart scheme for speeding up first-order methods
• NESTA: A Fast and Accurate First-Order Method for Sparse Recovery
• New tight frames of curvelets and optimal representations of objects with piecewise C² singularities
• Stable and Robust Sampling Strategies for Compressive Imaging
• Robustness to Unknown Error in Sparse Regularization
• Optimal Compressive Imaging of Fourier Data
• Ridgelets: a key to higher-dimensional intermittency?
• Compressive Imaging: Structure, Sampling, Learning
• Computational complexity versus statistical performance on sparse recovery problems
• Lipschitz Certificates for Layered Network Structures Driven by Averaged Activation Operators
• WARPd: A Linearly Convergent First-Order Primal-Dual Algorithm for Inverse Problems with Approximate Sharpness Conditions
• Sparse Polynomial Approximation of High-Dimensional Functions
• Sharpness, Restart, and Acceleration
• Solving inverse problems using data-driven models
• On the Role of Total Variation in Compressed Sensing
• Optimally Sparse Multidimensional Representation Using Shearlets
• Improved Recovery Guarantees and Sampling Strategies for TV Minimization in Compressive Imaging

This page was built for publication: NESTANets: stable, accurate and efficient neural networks for analysis-sparse inverse problems