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09/14/2023
Multi-Grade Deep Learning for Partial Differential Equations with Applications to the Burgers Equation
We develop in this paper a multi-grade deep learning method for solving ...
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06/02/2023
Uniform Convergence of Deep Neural Networks with Lipschitz Continuous Activation Functions and Variable Widths
We consider deep neural networks with a Lipschitz continuous activation ...
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05/13/2023
Successive Affine Learning for Deep Neural Networks
This paper introduces a successive affine learning (SAL) model for const...
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02/10/2023
A Non-gradient DG method for second-order Elliptic Equations in the Non-divergence Form
L^1 based optimization is widely used in image denoising, machine learni...
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02/01/2023
Multi-Grade Deep Learning
The current deep learning model is of a single-grade, that is, it learns...
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07/27/2022
Sparse Deep Neural Network for Nonlinear Partial Differential Equations
More competent learning models are demanded for data processing due to i...
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06/10/2022
Inverting Incomplete Fourier Transforms by a Sparse Regularization Model and Applications in Seismic Wavefield Modeling
We propose a sparse regularization model for inversion of incomplete Fou...
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05/13/2022
Convergence of Deep Neural Networks with General Activation Functions and Pooling
Deep neural networks, as a powerful system to represent high dimensional...
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11/15/2021
A Fast Convergent Ordered-Subsets Algorithm with Subiteration-Dependent Preconditioners for PET Image Reconstruction
We investigated the imaging performance of a fast convergent ordered-sub...
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09/28/2021
Convergence of Deep Convolutional Neural Networks
Convergence of deep neural networks as the depth of the networks tends t...
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07/27/2021
Convergence of Deep ReLU Networks
We explore convergence of deep neural networks with the popular ReLU act...
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06/06/2021
An L^p-weak Galerkin method for second order elliptic equations in non-divergence form
This article presents a new primal-dual weak Galerkin method for second ...
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02/18/2020
Multiplicative Noise Removal: Nonlocal Low-Rank Model and Its Proximal Alternating Reweighted Minimization Algorithm
The goal of this paper is to develop a novel numerical method for effici...
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06/13/2019
Dynamic PET cardiac and parametric image reconstruction: a fixed-point proximity gradient approach using patch-based DCT and tensor SVD regularization
Our aim was to enhance visual quality and quantitative accuracy of dynam...
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04/07/2011