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Michaël Unser

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Publications associées (506)

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Landmark-Based Shape Encoding and Sparse-Dictionary Learning in the Continuous Domain

Michaël Unser, Daniel Andreas Schmitter

We provide a generic framework to learn shape dictionaries of landmark-based curves that are defined in the continuous domain. We first present an unbiased alignment method that involves the construction of a mean shape as well as training sets whose eleme ...

2018

Shortest-support multi-spline bases for generalized sampling

Michaël Unser, Shayan Aziznejad, Alexis Marie Frederic Goujon

Generalized sampling consists in the recovery of a function f, from the samples of the responses of a collection of linear shift-invariant systems to the input f . The reconstructed function is typically a member of a finitely generated integer-shift invar ...

2021

A bulk modulus dependent linear model for acoustical imaging

Michaël Unser, Thierry Blu

Modeling the acoustical process of soft biological tissue imaging and understanding the consequences of the approximations required by. such modeling are key steps for accurately simulating ultrasonic scanning as well as estimating the scattering coefficie ...

ASA2009

CryoGAN: A New Reconstruction Paradigm for Single-Particle Cryo-EM Via Deep Adversarial Learning

Michaël Unser, Michael Thompson McCann, Laurène Donati, Harshit Gupta

We present CryoGAN, a new paradigm for single-particle cryo-electron microscopy (cryo-EM) reconstruction based on unsupervised deep adversarial learning. In single-particle cryo-EM, the structure of a biomolecule needs to be reconstructed from a large set ...

2021

Myocardial Motion Analysis from B-Mode Echocardiograms

Michaël Unser, Michael Sühling, Muthuvel Arigovindan

The quantitative assessment of cardiac motion is a fundamental concept to evaluate ventricular malfunction. We present a new optical-flow-based method for estimating heart motion from two-dimensional echocardiographic sequences. To account for typical hear ...

IEEE2005

Adaptive Image Resizing Based on Continuous-Domain Stochastic Modeling

Michaël Unser, Aurélien Bourquard, John Paul Ward, Hagay Kirshner

We introduce an adaptive continuous-domain modeling approach to texture and natural images. The continuous-domain image is assumed to be a smooth function, and we embed it in a parameterized Sobolev space. We point out a link between Sobolev spaces and sto ...

Ieee-Inst Electrical Electronics Engineers Inc2014

Nonideal Sampling and Interpolation from Noisy Observations in Shift-Invariant Spaces

Michaël Unser

Digital analysis and processing of signals inherently relies on the existence of methods for reconstructing a continuous-time signal from a sequence of corrupted discrete-time samples. In this paper, a general formulation of this problem is developed that ...

IEEE2006

Deep Neural Networks With Trainable Activations and Controlled Lipschitz Constant

Michaël Unser, Shayan Aziznejad, Harshit Gupta, Joaquim Gonçalves Garcia Barreto Campos

We introduce a variational framework to learn the activation functions of deep neural networks. Our aim is to increase the capacity of the network while controlling an upper-bound of the actual Lipschitz constant of the input-output relation. To that end, ...

2020

Reconstruction Of Biomedical Images And Sparse Stochastic Modeling

Michaël Unser, Emrah Bostan, Ulugbek Kamilov

We propose a novel statistical formulation of the image-reconstruction problem from noisy linear measurements. We derive an extended family of MAP estimators based on the theory of continuous-domain sparse stochastic processes. We highlight the crucial rol ...

Ieee2012

Deep Convolutional Neural Network for Inverse Problems in Imaging

Michaël Unser, Michael Thompson McCann, Kyong Hwan Jin, Emmanuel Augustin Julien Froustey

In this paper, we propose a novel deep convolutional neural network (CNN)-based algorithm for solving ill-posed inverse problems. Regularized iterative algorithms have emerged as the standard approach to ill-posed inverse problems in the past few decades. ...

2017

False Discovery Rate for Wavelet-Based Statistical Parametric Mapping

Michaël Unser, Dimitri Nestor Alice Van De Ville

Model-based statistical analysis of functional magnetic resonance imaging (fMRI) data relies on the general linear model and statistical hypothesis testing. Due to the large number of intracranial voxels, it is important to deal with the multiple compariso ...

IEEE2008

Time-Dependent Deep Image Prior for Dynamic MRI

Michaël Unser, Harshit Gupta, Kyong Hwan Jin, Jaejun Yoo

We propose a novel unsupervised deep-learning-based algorithm for dynamic magnetic resonance imaging (MRI) reconstruction. Dynamic MRI requires rapid data acquisition for the study of moving organs such as the heart. We introduce a generalized version of t ...

Institute of Electrical and Electronics Engineers2021

Cardinal Exponential Splines: Part I—Theory and Filtering Algorithms

Michaël Unser, Thierry Blu

Causal exponentials play a fundamental role in classical system theory. Starting from those elementary building blocks, we propose a complete and self-contained signal processing formulation of exponential splines defined on a uniform grid. We specify the ...

IEEE2005

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

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

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

Michaël Unser, Julien René Fageot, John Paul Ward

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

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Michaël Unser, Dimitri Nestor Alice Van De Ville, Daniel Sage

The monogenic signal is the natural 2-D counterpart of the 1-D analytic signal. We propose to transpose the concept to the wavelet domain by considering a complexified version of the Riesz transform which has the remarkable property of mapping a real-value ...

Institute of Electrical and Electronics Engineers2009

Fast multiscale reconstruction for Cryo-EM

Michaël Unser, Masih Nilchian, Laurène Donati

We present a multiscale reconstruction framework for single-particle analysis (SPA). The representation of three-dimensional (3D) objects with scaled basis functions permits the reconstruction of volumes at any desired scale in the real-space. This multisc ...

Elsevier2018

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

Sampling in Practice: Is the Best Reconstruction Space Bandlimited?

Michaël Unser, Dimitri Nestor Alice Van De Ville, Sathish Ramani

Shannon's sampling theory and its variants provide effective solutions to the problem of reconstructing a signal from its samples in some “shift-invariant” space, which may or may not be bandlimited. In this paper, we present some further justification for ...

IEEE2005