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Michaël Unser

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Publications associées (516)

Gaussian and sparse processes are limits of generalized Poisson processes

Michaël Unser, Virginie Sophie Uhlmann, Julien René Pierre Fageot

The theory of sparse stochastic processes offers a broad class of statistical models to study signals, far beyond the more classical class of Gaussian processes. In this framework, signals are represented as realizations of random processes that are soluti ...

2020

Dictionary Learning with Statistical Sparsity in the Presence of Noise

Michaël Unser, Shayan Aziznejad, Emmanuel Emilien Louis Soubies

We consider a new stochastic formulation of sparse representations that is based on the family of symmetric alpha-stable (S alpha S) distributions. Within this framework, we develop a novel dictionary-learning algorithm that involves a new estimation techn ...

IEEE2020

Deep Neural Networks With Trainable Activations and Controlled Lipschitz Constant

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

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

Computation of "Best" Interpolants in the Lp Sense

Michaël Unser, Pakshal Narendra Bohra

We study a variant of the interpolation problem where the continuously defined solution is regularized by minimizing the L p -norm of its second-order derivative. For this continuous-domain problem, we propose an exact discretization scheme that restricts ...

2020

Support and approximation properties of Hermite splines

Michaël Unser, Virginie Sophie Uhlmann, Julien René Pierre Fageot, Shayan Aziznejad

In this paper, we formally investigate two mathematical aspects of Hermite splines that are relevant to practical applications. We first demonstrate that Hermite splines are maximally localized, in the sense that the size of their support is minimal among ...

2020

Continuous-Domain Signal Reconstruction Using L-p-Norm Regularization

Michaël Unser, Pakshal Narendra Bohra

We focus on the generalized-interpolation problem. There, one reconstructs continuous-domain signals that honor discrete data constraints. This problem is infinite-dimensional and ill-posed. We make it well-posed by imposing that the solution balances data ...

2020

Learning Activation Functions in Deep (Spline) Neural Networks

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

We develop an efficient computational solution to train deep neural networks (DNN) with free-form activation functions. To make the problem well-posed, we augment the cost functional of the DNN by adding an appropriate shape regularization: the sum of the ...

2020

A method for assessing the fidelity of optical diffraction tomography reconstruction methods using structured illumination

Michaël Unser, Demetri Psaltis, Thanh-An Michel Pham, Ahmed Ayoub, Joowon Lim

2020

A Note on BIBO Stability

Michaël Unser

The statements on the BIBO stability of continuoustime convolution systems found in engineering textbooks are often either too vague (because of lack of hypotheses) or mathematically incorrect. What is more troubling is that they usually exclude the identi ...

2020

Deep-learning projector for optical diffraction tomography

Michaël Unser, Thanh-An Michel Pham, Harshit Gupta, Fangshu Yang

Optical diffraction tomography is an effective tool to estimate the refractive indices of unknown objects. It proceeds by solving an ill-posed inverse problem for which the wave equation governs the scattering events. The solution has traditionally been de ...

2020

Multi-CryoGAN: Reconstruction of Continuous Conformations in Cryo-EM Using Generative Adversarial Networks

Michaël Unser, Harshit Gupta, Thanh Hai Phan, Jaejun Yoo

We propose a deep-learning-based reconstruction method for cryo-electron microscopy (Cryo-EM) that can model multiple conformations of a nonrigid biomolecule in a standalone manner. Cryo-EM produces many noisy projections from separate instances of the sam ...

Springer, Cham2020

Generating Sparse Stochastic Processes Using Matched Splines

Michaël Unser, Shayan Aziznejad, Leello Tadesse Dadi

We provide an algorithm to generate trajectories of sparse stochastic processes that are solutions of linear ordinary differential equations driven by Levy white noises. A recent paper showed that these processes are limits in law of generalized compound-P ...

2020

The n-term Approximation of Periodic Generalized Levy Processes

Michaël Unser, John Paul Ward, Julien René Pierre Fageot

In this paper, we study the compressibility of random processes and fields, called generalized Levy processes, that are solutions of stochastic differential equations driven by d-dimensional periodic Levy white noises. Our results are based on the estimati ...

2020

Multimodal imaging and high-throughput image-processing for drug screening on living organisms on-chip

Martinus Gijs, Michaël Unser, Virginie Sophie Uhlmann, Johan Auwerx, Matteo Cornaglia, Laurent Mouchiroud, Daniel Migliozzi

A major step for the validation of medical drugs is the screening on whole organisms, which gives the systemic information that is missing when using cellular models. Caenorhabditis elegans is a soil worm that catches the interest of researchers who study ...

SPIE Society of Photo-optical Instrumentation Engineers2019

Super-resolution fight club: assessment of 2D and 3D single-molecule localization microscopy software

Michaël Unser, Daniel Sage, Ricardo Henriques, Thanh-An Michel Pham, Thomas Pengo, Seamus John Holden, Tomas Lukes, Anna Archetti, Silvia Colabrese, Anurag Agrawal

With the widespread uptake of two-dimensional (2D) and three-dimensional (3D) single-molecule localization microscopy (SMLM), a large set of different data analysis packages have been developed to generate super-resolution images. In a large community effo ...

2019

Deforming Tessellations for the Segmentation of Cell Aggregates

Michaël Unser, Daniel Sage, Aymeric Alexandre Galan, Anaïs Laure Marie-Thérèse Badoual

We present a new active contour to segment cell aggregates. We describe it by a smooth tessellation that is attracted toward the cell membranes. Our approach relies on subdivision schemes that are tightly linked to the theory of wavelets. The shape is enco ...

IEEE2019

Angular Accuracy of Steerable Feature Detectors

Michaël Unser, Arash Amini, Zsuzsanna Püspöki, John Paul Ward, Julien René Pierre Fageot

The detection of landmarks or patterns is of interest for extracting features in biological images. Hence, algorithms for finding these keypoints have been extensively investigated in the literature, and their localization and detection properties are well ...

SIAM PUBLICATIONS2019

Scaling Limits of Solutions of Linear Stochastic Differential Equations Driven by Levy White Noises

Michaël Unser, Julien René Pierre Fageot

Consider a random process s that is a solution of the stochastic differential equation Ls = w with L a homogeneous operator and w a multidimensional Levy white noise. In this paper, we study the asymptotic effect of zooming in or zooming out of the process ...

2019

Normal-Based Interpolating Subdivision For The Geometric Representation Of Deformable Models

Michaël Unser, Anaïs Laure Marie-Thérèse Badoual

We review the normal-based interpolating subdivision scheme proposed in [1]. We show that it allows the user to exactly represent circles/spheres whenever suitable initial data are provided, and we also prove that it enjoys the property of similarity invar ...

IEEE2019

Sparse Dictionaries for Continuous-Domain Inverse Problems

Michaël Unser, Shayan Aziznejad, Thomas Jean Debarre

We study 1D continuous-domain inverse problems for multicomponent signals. The prior assumption on these signals is that each component is sparse in a different dictionary specified by a regularization operators. We introduce a hybrid regularization functi ...

2019

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