4 citations · 9 across the 9 of their papers we have counts for
9 papers
Controlled Learning of Pointwise Nonlinearities in Neural-Network-Like Architectures
Michael Unser, Alexis Goujon, Stanislas Ducotterd
We present a general variational framework for the training of freeform nonlinearities in layered computational architectures subject to some slope constraints. The regularization…
Learning Weakly Convex Regularizers for Convergent Image-Reconstruction Algorithms
Alexis Goujon, Sebastian Neumayer, Michael Unser
We propose to learn non-convex regularizers with a prescribed upper bound on their weak-convexity modulus. Such regularizers give rise to variational denoisers that minimize a conv…
A Neural-Network-Based Convex Regularizer for Inverse Problems
Alexis Goujon, Sebastian Neumayer, Pakshal Bohra +2
The emergence of deep-learning-based methods to solve image-reconstruction problems has enabled a significant increase in reconstruction quality. Unfortunately, these new methods o…
Improving Lipschitz-Constrained Neural Networks by Learning Activation Functions
Stanislas Ducotterd, Alexis Goujon, Pakshal Bohra +3
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 lear…
Delaunay-Triangulation-Based Learning with Hessian Total-Variation Regularization
Mehrsa Pourya, Alexis Goujon, Michael Unser
Regression is one of the core problems tackled in supervised learning. Rectified linear unit (ReLU) neural networks generate continuous and piecewise-linear (CPWL) mappings and are…
On the Number of Regions of Piecewise Linear Neural Networks
Alexis Goujon, Arian Etemadi, Michael Unser
Many feedforward neural networks (NNs) generate continuous and piecewise-linear (CPWL) mappings. Specifically, they partition the input domain into regions on which the mapping is…
Approximation of Lipschitz Functions using Deep Spline Neural Networks
Sebastian Neumayer, Alexis Goujon, Pakshal Bohra +1
Lipschitz-constrained neural networks have many applications in machine learning. Since designing and training expressive Lipschitz-constrained networks is very challenging, there…
Stable Parametrization of Continuous and Piecewise-Linear Functions
Alexis Goujon, Joaquim Campos, Michael Unser
Rectified-linear-unit (ReLU) neural networks, which play a prominent role in deep learning, generate continuous and piecewise-linear (CPWL) functions. While they provide a powerful…
Shortest-support Multi-Spline Bases for Generalized Sampling
Alexis Goujon, Shayan Aziznejad, Alireza Naderi +1
Generalized sampling consists in the recovery of a function , from the samples of the responses of a collection of linear shift-invariant systems to the input . The reconstru…