Home

Person

Michaël Unser

About
Privacy
Disclaimer

Graph Chatbot

Related publications (516)

Beyond Wiener's Lemma: Nuclear Convolution Algebras and the Inversion of Digital Filters

Michaël Unser, John Paul Ward, Julien René Pierre Fageot

A convolution algebra is a topological vector space X that is closed under the convolution operation. It is said to be inverse-closed if each element of X whose spectrum is bounded away from zero has a convolution inverse that is also part of the algebra. ...

SPRINGER BIRKHAUSER2019

Imaging cellular ultrastructures using expansion microscopy (U-ExM)

Michaël Unser, Virginie Hamel, Paul Guichard, Denis Fortun, Davide Gambarotto

Determining the structure and composition of macromolecular assemblies is a major challenge in biology. Here we describe ultrastructure expansion microscopy (U-ExM), an extension of expansion microscopy that allows the visualization of preserved ultrastruc ...

2019

Optimal Spline Generators for Derivative Sampling

Michaël Unser, Shayan Aziznejad, Alireza Naderi

The goal of derivative sampling is to reconstruct a signal from the samples of the function and of its first-order derivative. In this paper, we consider this problem over a shift-invariant reconstruction subspace generated by two compact-support functions ...

IEEE2019

Deep Spline Networks With Control Of Lipschitz Regularity

Michaël Unser, Shayan Aziznejad

The motivation for this work is to improve the performance of deep neural networks through the optimization of the individual activation functions. Since the latter results in an infinite-dimensional optimization problem, we resolve the ambiguity by search ...

IEEE2019

System and method for performing isogeometric analysis and finite element analysis using h-splines

Michaël Unser, Daniel Andreas Schmitter, Zsuzsanna Püspöki

A method for performing H-spline compatible isogeometric analysis (IGA) on a geometric object, the method being performed on a computer device having a memory, the method including the steps of creating an analysis suitable geometry (ASG) using H-splines f ...

2019

Closed-Form Expression of the Fourier Ring-Correlation for Single-Molecule Localization Microscopy

Michaël Unser, Daniel Sage, Thanh-An Michel Pham, Emmanuel Emilien Louis Soubies

Single-molecule localization microscopy (SMLM) is a popular microscopic technique that achieves super resolution imaging by localizing individual blinking molecules in thousands of frames. Therefore, the reconstructed high-resolution image is a combination ...

IEEE2019

Pocket guide to solve inverse problems with GlobalBioIm

Michaël Unser, Daniel Sage, Laurène Donati, Thanh-An Michel Pham, Ferréol Arnaud Marie Soulez, Michael Thompson McCann, Emmanuel Emilien Louis Soubies, Thomas Jean Debarre

GlobalBioIm is an open-source MATLAB (R) library for solving inverse problems. The library capitalizes on the strong commonalities between forward models to standardize the resolution of a wide range of imaging inverse problems. Endowed with an operator-al ...

2019

Biomedical Image Reconstruction: From the Foundations to Deep Neural Networks

Michaël Unser, Michael Thompson McCann

This tutorial covers biomedical image reconstruction, from the foundational concepts of system modeling and direct reconstruction to modern sparsity and learning-based approaches. Imaging is a critical tool in biological research and medicine, and most ima ...

2019

Solving Continuous-Domain Problems Exactly with Multiresolution B-Splines

Michaël Unser, Julien René Pierre Fageot, Harshit Gupta, Thomas Jean Debarre

We propose a discretization method for continuous-domain linear inverse problems with multiple-order total-variation (TV) regularization. It is based on a recent result that proves that such inverse problems have sparse polynomial-spline solutions. Our met ...

IEEE2019

Approximation of Non-decaying Signals from Shift-Invariant Subspaces

Michaël Unser, Quy Ha Nguyen

In our recent work, the sampling and reconstruction of non-decaying signals, modeled as members of weighted-L-p spaces, were shown to be stable with an appropriate choice of the generating kernel for the shift-invariant reconstruction space. In this paper, ...

2019

Method and system for the creation of an h-spline based data structure, data storage, and data representation

Michaël Unser, Daniel Andreas Schmitter, Zsuzsanna Püspöki

A method for generating a data structure to digitally represent a geometrical object based on H-splines, the method being performed on a computer device having a data processor and memory, the method including the steps of creating a first data structure a ...

2019

Computational Super-Sectioning for Single-Slice Structured-Illumination Microscopy

Michaël Unser, Emmanuel Emilien Louis Soubies

While structured-illumination microscopy (SIM) is inherently a three-dimensional (3-D) technique, many biological questions can be addressed from the acquisition of a single focal plane with high lateral resolution. Unfortunately, the single-slice reconstr ...

2019

Hybrid-Spline Dictionaries for Continuous-Domain Inverse Problems

Michaël Unser, Shayan Aziznejad, Thomas Jean Debarre

We study one-dimensional continuous-domain inverse problems with multiple generalized total-variation regularization, which involves the joint use of several regularization operators. Our starting point is a new representer theorem that states that such in ...

2019

A Representer Theorem for Deep Neural Networks

Michaël Unser

We propose to optimize the activation functions of a deep neural network by adding a corresponding functional regularization to the cost function. We justify the use of a second-order total-variation criterion. This allows us to derive a general represente ...

2019

Inner-Loop-Free ADMM for Cryo-EM

Michaël Unser, Laurène Donati, Emmanuel Emilien Louis Soubies

Thanks to recent advances in signal processing, the interest for fast ℓ1-regularized reconstruction algorithms in cryo-electron microscopy (cryo-EM) has intensified. The approaches based on the alternating-direction of multipliers method (ADMM) are particu ...

IEEE2019

B-Spline-Based Exact Discretization of Continuous-Domain Inverse Problems With Generalized TV Regularization

Michaël Unser, Julien René Pierre Fageot, Harshit Gupta, Thomas Jean Debarre

We study continuous-domain linear inverse problems with generalized total-variation (gTV) regularization, expressed in terms of a regularization operator L. It has recently been proved that such inverse problems have sparse spline solutions, with fewer jum ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2019

Texture-driven parametric snakes for semi-automatic image segmentation

Michaël Unser, Adrien Raphaël Depeursinge, Anaïs Laure Marie-Thérèse Badoual

We present a texture-driven parametric snake for semi-automatic segmentation of a single and closed structure in an image. We propose a new energy functional that combines intensity and texture information. The two types of image information are balanced u ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2019

Learning Tomography Assessed Using Mie Theory

Michaël Unser, Demetri Psaltis, Joowon Lim

In optical diffraction tomography, the multiply scattered field is a nonlinear function of the refractive index (RI) of the object. The Rytov method relies on a single-scattering propagation model and is commonly used to reconstruct images. Recently, a rec ...

American Physical Society (APS)2018

Rotation Invariance and Directional Sensitivity: Spherical Harmonics versus Radiomics Features

Michaël Unser, Adrien Raphaël Depeursinge, John Paul Ward, Julien René Pierre Fageot

We define and investigate the Local Rotation Invariance (LRI) and Directional Sensitivity (DS) of radiomics features. Most of the classical features cannot combine the two properties, which are antagonist in simple designs. We propose texture operators bas ...

SPRINGER INTERNATIONAL PUBLISHING AG2018

Imaging neural activity in the ventral nerve cord of behaving adult Drosophila

Michaël Unser, Pavan P Ramdya, Denis Fortun, Chin-Lin Chen, Laura Joan Hermans, Florian Aymanns

To understand neural circuits that control limbs, one must measure their activity during behavior. Until now this goal has been challenging, because limb premotor and motor circuits have been largely inaccessible for large-scale recordings in intact, movin ...

Nature Research2018

Page 6 of 26