Parseval proximal neural networks

DOI10.1007/s00041-020-09761-7zbMath1489.68224arXiv1912.10480OpenAlexW2994632629MaRDI QIDQ785901

Marzieh Hasannasab, Simon Setzer, Johannes Hertrich, Sebastian Neumayer, Gabriele Drauschke, Gerlind Plonka-Hoch

Publication date: 12 August 2020

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.10480

zbMATH Keywords

proximal operatorsframe shrinkageadverserial robustnessaveraged operatorsLipschitz neural networksoptimization on Stiefel manifolds

Mathematics Subject Classification ID

Nonconvex programming, global optimization (90C26) Learning and adaptive systems in artificial intelligence (68T05)

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Cites Work

• Unnamed Item
• Unnamed Item
• A feasible method for optimization with orthogonality constraints
• Operator splittings, Bregman methods and frame shrinkage in image processing
• Variable metric forward-backward algorithm for minimizing the sum of a differentiable function and a convex function
• Incremental proximal methods for large scale convex optimization
• Weak convergence theorems for nonexpansive mappings in Banach spaces
• Monotone operator theory in convex optimization
• On the rotational invariant \(L_1\)-norm PCA
• First-Order Methods in Optimization
• A Convergent Image Fusion Algorithm Using Scene-Adapted Gaussian-Mixture-Based Denoising
• An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
• On the Equivalence of Soft Wavelet Shrinkage, Total Variation Diffusion, Total Variation Regularization, and SIDEs
• A MULTISCALE WAVELET-INSPIRED SCHEME FOR NONLINEAR DIFFUSION
• First Order Algorithms in Variational Image Processing
• Signal Recovery by Proximal Forward-Backward Splitting
• Proximité et dualité dans un espace hilbertien
• Convex analysis and monotone operator theory in Hilbert spaces
• An introduction to frames and Riesz bases

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