Search Results for author: Alexis Goujon

Found 7 papers, 4 papers with code

Learning Weakly Convex Regularizers for Convergent Image-Reconstruction Algorithms

2 code implementations21 Aug 2023 Alexis Goujon, Sebastian Neumayer, Michael Unser

We propose to learn non-convex regularizers with a prescribed upper bound on their weak-convexity modulus.

MRI Reconstruction

A Neural-Network-Based Convex Regularizer for Inverse Problems

2 code implementations22 Nov 2022 Alexis Goujon, Sebastian Neumayer, Pakshal Bohra, Stanislas Ducotterd, Michael Unser

The emergence of deep-learning-based methods to solve image-reconstruction problems has enabled a significant increase in reconstruction quality.

Denoising MRI Reconstruction

Improving Lipschitz-Constrained Neural Networks by Learning Activation Functions

1 code implementation28 Oct 2022 Stanislas Ducotterd, Alexis Goujon, Pakshal Bohra, Dimitris Perdios, Sebastian Neumayer, Michael Unser

Lipschitz-constrained neural networks have several advantages over unconstrained ones and can be applied to a variety of problems, making them a topic of attention in the deep learning community.

Delaunay-Triangulation-Based Learning with Hessian Total-Variation Regularization

1 code implementation16 Aug 2022 Mehrsa Pourya, Alexis Goujon, Michael Unser

Rectified linear unit (ReLU) neural networks generate continuous and piecewise-linear (CPWL) mappings and are the state-of-the-art approach for solving regression problems.


On the Number of Regions of Piecewise Linear Neural Networks

no code implementations17 Jun 2022 Alexis Goujon, Arian Etemadi, Michael Unser

We first provide upper and lower bounds on the maximal number of linear regions of a CPWL NN given its depth, width, and the number of linear regions of its activation functions.

Approximation of Lipschitz Functions using Deep Spline Neural Networks

no code implementations13 Apr 2022 Sebastian Neumayer, Alexis Goujon, Pakshal Bohra, Michael Unser

Lipschitz-constrained neural networks have many applications in machine learning.

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