Publications de Sebastian Jonas Neumayer

Learning a Convex Patch-Based Synthesis Model via Deep Equilibrium

Michaël Unser, Sebastian Jonas Neumayer, Stanislas Ducotterd

We investigate the learning of a convex patch-based synthesis model for the reconstruction of images. In essence, we propose to learn a dictionary via bilevel optimization for denoising. Using implicit differentiation, we find a closed-form formula of the ...

IEEE2024

Template-Based Image Reconstruction Facing Different Topologies

Sebastian Jonas Neumayer

The reconstruction of images from measured data is an increasing field of research. For highly under-determined problems, template-based image reconstruction provides a way of compensating for the lack of sufficient data. A caveat of this approach is that ...

Springer/Plenum Publishers2024

On the Effect of Initialization: The Scaling Path of 2-Layer Neural Networks

Michaël Unser, Sebastian Jonas Neumayer, Lénaïc Chizat

In supervised learning, the regularization path is sometimes used as a convenient theoretical proxy for the optimization path of gradient descent initialized from zero. In this paper, we study a modification of the regularization path for infinite-width 2- ...

2024

Improving Lipschitz-Constrained Neural Networks by Learning Activation Functions

Michaël Unser, Dimitris Perdios, Pakshal Narendra Bohra, Alexis Marie Frederic Goujon, Sebastian Jonas Neumayer, Stanislas Ducotterd

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. Unfortunately, it has been shown both theoretically and empi ...

2024

Learning Weakly Convex Regularizers for Convergent Image-Reconstruction Algorithms

Michaël Unser, Alexis Marie Frederic Goujon, Sebastian Jonas Neumayer

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 convex energy. They rely on few parameters (less than 15,000) and offer a signal ...

2024

A Neural-Network-Based Convex Regularizer for Inverse Problems

Michaël Unser, Pakshal Narendra Bohra, Alexis Marie Frederic Goujon, Sebastian Jonas Neumayer, Stanislas Ducotterd

The emergence of deep-learning-based methods to solve image-reconstruction problems has enabled a significant increase in quality. Unfortunately, these new methods often lack reliability and explainability, and there is a growing interest to address these ...

2023

Data for: "A Neural-Network-Based Convex Regularizer for Inverse Problems"

Michaël Unser, Pakshal Narendra Bohra, Alexis Marie Frederic Goujon, Sebastian Jonas Neumayer, Stanislas Ducotterd

Data for: "A Neural-Network-Based Convex Regularizer for Inverse Problems". The corresponding scripts can be accessed on GitHub (https://github.com/axgoujon/convex_ridge_regularizers). The data is organized as follows: - ct_data_sets.tar.gz: contains prepr ...

Zenodo2023

Approximation of Lipschitz Functions Using Deep Spline Neural Networks

Michaël Unser, Pakshal Narendra Bohra, Alexis Marie Frederic Goujon, Sebastian Jonas Neumayer

Although Lipschitz-constrained neural networks have many applications in machine learning, the design and training of expressive Lipschitz-constrained networks is very challenging. Since the popular rectified linear-unit networks have provable disadvantage ...

2023

Stability of Image-Reconstruction Algorithms

Michaël Unser, Sebastian Jonas Neumayer, Pol del Aguila Pla

Robustness and stability of image-reconstruction algorithms have recently come under scrutiny. Their importance to medical imaging cannot be overstated. We review the known results for the topical variational regularization strategies ( ℓ2 and ℓ1 regulariz ...

2023

Explicit representations for Banach subspaces of Lizorkin distributions

Michaël Unser, Sebastian Jonas Neumayer

The Lizorkin space is well suited to the study of operators like fractional Laplacians and the Radon transform. In this paper, we show that the space is unfortunately not complemented in the Schwartz space. In return, we show that it is dense in C0(Double- ...

2023