52 citations · 192 across the 24 of their papers we have counts for
28 papers
A sharp bound for sampling widths in the uniform norm: kernel -optimal designs and oversampling
Sebastian Neumayer, Tino Ullrich
For every reproducing kernel Hilbert space with bounded kernel , we prove that the linear sampling widths and Gelfand widths in the unif…
Greedy sampling designs via reduced basis methods: optimal recovery in the uniform norm
Sebastian Neumayer, Kateryna Pozharska, Tino Ullrich
We study optimal sampling recovery in reproducing kernel Hilbert spaces (RKHS) in the uniform norm. For every RKHS with bounded kernel, we establish new comparisons between linear…
High-dimensional sparse recovery from function samples - Decoders, guarantees and instance optimality
Moritz Moeller, Sebastian Neumayer, Kateryna Pozharska +2
We investigate the reconstruction of multivariate functions from samples using sparse recovery techniques. For Square Root Lasso, Orthogonal Matching Pursuit, and Compressive Sampl…
Wasserstein Gradient Flows for Moreau Envelopes of f-Divergences in Reproducing Kernel Hilbert Spaces
Viktor Stein, Sebastian Neumayer, Nicolaj Rux +1
Commonly used -divergences of measures, e.g., the Kullback-Leibler divergence, are subject to limitations regarding the support of the involved measures. A remedy is regularizin…
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…
On the Effect of Initialization: The Scaling Path of 2-Layer Neural Networks
Sebastian Neumayer, Lénaïc Chizat, Michael Unser
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 pap…
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…
Stability of Image-Reconstruction Algorithms
Pol del Aguila Pla, Sebastian Neumayer, Michael Unser
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…
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…
Explicit representations for Banach subspaces of Lizorkin distributions
Sebastian Neumayer, Michael Unser
The Lizorkin space is well-suited for studying various operators; e.g., fractional Laplacians and the Radon transform. In this paper, we show that the space is unfortunately not co…
Template-Based Image Reconstruction Facing Different Topologies
Sebastian Neumayer, Antonia Topalovic
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 comp…
An Image Registration Model in Electron Backscatter Diffraction
Manuel Gräf, Sebastian Neumayer, Ralf Hielscher +3
Recently, variational methods were successfully applied for computing the optical flow in gray and RGB-valued image sequences. A crucial assumption in these models is that pixel-va…
Unbalanced Multi-Marginal Optimal Transport
Florian Beier, Johannes von Lindheim, Sebastian Neumayer +1
Entropy regularized optimal transport and its multi-marginal generalization have attracted increasing attention in various applications, in particular due to efficient Sinkhorn-lik…
Convolutional Proximal Neural Networks and Plug-and-Play Algorithms
Johannes Hertrich, Sebastian Neumayer, Gabriele Steidl
In this paper, we introduce convolutional proximal neural networks (cPNNs), which are by construction averaged operators. For filters of full length, we propose a stochastic gradie…
Stabilizing Invertible Neural Networks Using Mixture Models
Paul Hagemann, Sebastian Neumayer
In this paper, we analyze the properties of invertible neural networks, which provide a way of solving inverse problems. Our main focus lies on investigating and controlling the Li…
Transfer Operators from Optimal Transport Plans for Coherent Set Detection
Péter Koltai, Johannes von Lindheim, Sebastian Neumayer +1
The topic of this study lies in the intersection of two fields. One is related with analyzing transport phenomena in complicated flows.For this purpose, we use so-called coherent s…
From Optimal Transport to Discrepancy
Sebastian Neumayer, Gabriele Steidl
A common way to quantify the ,,distance'' between measures is via their discrepancy, also known as maximum mean discrepancy (MMD). Discrepancies are related to Sinkhorn divergences…
Parseval Proximal Neural Networks
Marzieh Hasannasab, Johannes Hertrich, Sebastian Neumayer +3
The aim of this paper is twofold. First, we show that a certain concatenation of a proximity operator with an affine operator is again a proximity operator on a suitable Hilbert sp…
Frame Soft Shrinkage as Proximity Operator
Marzieh Hassanasab, Sebastian Neumayer, Gerlind Plonka +3
Let and be real Hilbert spaces and an injective operator with closed range and Moore-Penrose inverse $T^\dagge…
Curve Based Approximation of Measures on Manifolds by Discrepancy Minimization
Martin Ehler, Manuel Gräf, Sebastian Neumayer +1
The approximation of probability measures on compact metric spaces and in particular on Riemannian manifoldsby atomic or empirical ones is a classical task in approximation and com…
Minimal Lipschitz and -Harmonic Extensions of Vector-Valued Functions on Finite Graphs
Miroslav Bačák, Johannes Hertrich, Sebastian Neumayer +1
This paper deals with extensions of vector-valued functions on finite graphs fulfilling distinguished minimality properties. We show that so-called lex and L-lex minimal extensions…
On the Robust PCA and Weiszfeld's Algorithm
Sebastian Neumayer, Max Nimmer, Simon Setzer +1
Principal component analysis (PCA) is a powerful standard tool for reducing the dimensionality of data. Unfortunately, it is sensitive to outliers so that various robust PCA varian…
Convergence of the Time Discrete Metamorphosis Model on Hadamard Manifolds
Alexander Effland, Sebastian Neumayer, Martin Rumpf
Continuous image morphing is a classical task in image processing. The metamorphosis model proposed by Trouvé, Younes and coworkers casts this problem in the frame of Riemannian ge…