Michaël Unser

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Deep-prior ODEs augment fluorescence imaging with chemical sensors

Michaël Unser

To study biological signalling, great effort goes into designing sensors whose fluorescence follows the concentration of chemical messengers as closely as possible. However, the binding kinetics of the sensors are often overlooked when interpreting cell si ...

Nature Research2024

Complex-order scale-invariant operators and self-similar processes

Michaël Unser, Julien René Pierre Fageot

In this paper, we perform the joint study of scale -invariant operators and self -similar processes of complex order. More precisely, we introduce general families of scale -invariant complex -order fractional -derivation and integration operators by const ...

Academic Press Inc Elsevier Science2024

On the number of regions of piecewise linear neural networks

Michaël Unser, Alexis Marie Frederic Goujon

Many feedforward neural networks (NNs) generate continuous and piecewise-linear (CPWL) mappings. Specifically, they partition the input domain into regions on which the mapping is affine. The number of these so-called linear regions offers a natural metric ...

2024

Surpassing light inhomogeneities in structured-illumination microscopy with FlexSIM

Michaël Unser, Daniel Sage

Super-resolution structured-illumination microscopy (SIM) is a powerful technique that allows one to surpass the diffraction limit by up to a factor two. Yet, its practical use is hampered by its sensitivity to imaging conditions which makes it prone to re ...

2024

DISTRIBUTIONAL EXTENSION AND INVERTIBILITY OF THE k-PLANE TRANSFORM AND ITS DUAL

Michaël Unser, Rahul Parhi

We investigate the distributional extension of the k-plane transform in Rd and of related operators. We parameterize the k-plane domain as the Cartesian product of the Stiefel manifold of orthonormal k-frames in Rd with Rd-k. This parameterization imposes ...

2024

A Box-Spline Framework for Inverse Problems With Continuous-Domain Sparsity Constraints

Michaël Unser, Mehrsa Pourya

The formulation of inverse problems in the continuum eliminates discretization errors and allows for the exact incorporation of priors. In this paper, we formulate a continuous-domain inverse problem over a search space of continuous and piecewise-linear f ...

Ieee-Inst Electrical Electronics Engineers Inc2024

Sensitivity-Aware Density Estimation in Multiple Dimensions

Michaël Unser, Pol del Aguila Pla

We formulate an optimization problem to estimate probability densities in the context of multidimensional problems that are sampled with uneven probability. It considers detector sensitivity as an heterogeneous density and takes advantage of the computatio ...

IEEE COMPUTER SOC2024

On the Effect of Initialization: The Scaling Path of 2-Layer Neural Networks

Michaël Unser, Sebastian Jonas Neumayer, Lénaïc Chizat

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 paper, we study a modification of the regularization path for infinite-width 2- ...

2024

Improving Lipschitz-Constrained Neural Networks by Learning Activation Functions

Michaël Unser, Dimitris Perdios, Pakshal Narendra Bohra, Alexis Marie Frederic Goujon, Sebastian Jonas Neumayer, Stanislas Ducotterd

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 learning community. Unfortunately, it has been shown both theoretically and empi ...

2024

Iteratively Refined Image Reconstruction with Learned Attentive Regularizers

Michaël Unser, Mehrsa Pourya

We propose a regularization scheme for image reconstruction that leverages the power of deep learning while hinging on classic sparsity-promoting models. Many deep-learning-based models are hard to interpret and cumbersome to analyze theoretically. In cont ...

2024

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