Michaël Unser

À propos
Confidentialité
Mentions légales

Graph Chatbot

Publications associées (516)

PET REBINNING WITH REGULARIZED DENSITY SPLINES

Michaël Unser

PET reconstruction algorithms have long relied on sinogram rebinning. However, as detectors grow smaller in a recent wave of cutting-edge scanners, individual sensors no longer accrue hundreds of photons. Instead, most detect a single photon or none at all ...

IEEE2023

A Statistical Framework to Investigate the Optimality of Signal-Reconstruction Methods

Michaël Unser, Pakshal Narendra Bohra, Pol del Aguila Pla

We present a statistical framework to benchmark the performance of reconstruction algorithms for linear inverse problems, in particular, neural-network-based methods that require large quantities of training data. We generate synthetic signals as realizati ...

2023

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

From Kernel Methods to Neural Networks: A Unifying Variational Formulation

Michaël Unser

The minimization of a data-fidelity term and an additive regularization functional gives rise to a powerful framework for supervised learning. In this paper, we present a unifying regularization functional that depends on an operator L\documentclass[12pt]{ ...

Springer2023

Stable parameterization of continuous and piecewise-linear functions

Michaël Unser, Alexis Marie Frederic Goujon, Joaquim Gonçalves Garcia Barreto Campos

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 parametric representation, the mapping between the parameter and function s ...

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

PROBING INTRACELLULAR ELASTICITY WITH MINIMAL-HESSIAN REGISTRATION

Michaël Unser

We propose an image-based elastography method to measure the heterogeneous stiffness inside a cell and its nucleus. It uses a widely accessible setup consisting of plate compression imaged with fluorescence microscopy. Our framework recovers a spatial map ...

IEEE2023

Ridges, Neural Networks, and the Radon Transform

Michaël Unser

A ridge is a function that is characterized by a one-dimensional profile (activation) and a multidimensional direction vector. Ridges appear in the theory of neural networks as functional descriptors of the effect of a neuron, with the direction vector bei ...

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

Boosting Weakly Convex Ridge Regularizers with Spatial Adaptivity

Michaël Unser, Alexis Marie Frederic Goujon, Sebastian Jonas Neumayer, Mehrsa Pourya

2023

Page 4 sur 52