Publications by Michaël Unser

Convergence analysis of the discretization of continuous-domain inverse problems

Michaël Unser, Julien René Pierre Fageot

We study continuous-domain linear inverse problems that involve a general data-fidelity term and a regularisation term. We consider a regularisation that is formed by the sparsity-promoting total-variation norm, pre-composed with a differential operator th ...

2025

Estimation of Stiffness Maps in Deforming Cells Through Optical Flow With Bounded Curvature

Michaël Unser

The stiffness of cells and of their nuclei is a biomarker of several pathological conditions. Current measurement methods rely on invasive physical probes that yield one or two stiffness values for the whole cell. However, the internal distribution of cell ...

Institute of Electrical and Electronics Engineers2025

Point-spread-function engineering in MINFLUX: optimality of donut and half-moon excitation patterns

Michaël Unser, Jonathan Yuelin Dong

Localization microscopy enables imaging with resolutions that surpass the conventional optical diffraction limit. Notably, the Maximally INFormative LUminescence eXcitation (MINFLUX) method achieves super-resolution by shaping the excitation point spread f ...

2025

A Silicon-Pixel Paradigm for PET

Michaël Unser, Pol del Aguila Pla, Jonathan Yuelin Dong

Positron emission tomography (PET) scanners use scintillation crystals to stop high-energy photons. The ensuing lower-energy photons are then detected via photomultipliers. We study the performance of a stack of monolithic siliconpixel detectors as an alte ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2025

Model-based temporal unmixing towards quantitative photo-switching optoacoustic tomography

Michaël Unser, Jonathan Yuelin Dong

Optoacoustic (OA) imaging combined with reversibly photoswitchable proteins has emerged as a promising technology for the high-sensitivity and multiplexed imaging of cells in live tissues in preclinical research. Through carefully designed illumination sch ...

2025

Structured Random Model for Fast and Robust Phase Retrieval

Michaël Unser, Jonathan Yuelin Dong

Phase retrieval, a nonlinear problem prevalent in imaging applications, has been extensively studied using random models, some of which with i.i.d. sensing matrix components. While these models offer robust reconstruction guarantees, they are computational ...

Institute of Electrical and Electronics Engineers Inc.2025

Function-Space Optimality of Neural Architectures with Multivariate Nonlinearities

Michaël Unser, Rahul Parhi

We investigate the function-space optimality (specifically, the Banach-space optimality) of a large class of shallow neural architectures with multivariate nonlinearities/activation functions. To that end, we construct a new family of Banach spaces defined ...

SIAM PUBLICATIONS2025

Controlled learning of pointwise nonlinearities in neural-network-like architectures

Michaël Unser, Stanislas Ducotterd, Alexis Marie Frederic Goujon

We present a general variational framework for the training of freeform nonlinearities in layered computational architectures subject to some slope constraints. The regularization that we add to the traditional training loss penalizes the second-order tota ...

2025

Learning a Convex Patch-Based Synthesis Model via Deep Equilibrium

Michaël Unser, Stanislas Ducotterd, Sebastian Jonas Neumayer

We investigate the learning of a convex patch-based synthesis model for the reconstruction of images. In essence, we propose to learn a dictionary via bilevel optimization for denoising. Using implicit differentiation, we find a closed-form formula of the ...

IEEE2024

A Continuous-Domain Solution for Computed Tomography with Hessian Total-Variation Regularization

Michaël Unser, Mehrsa Pourya, Youssef Haouchat

We formulate computed-tomography reconstruction as a continuous-domain optimization problem with Hessian total variation (HTV) as the regularizer. HTV is a sparsity-promoting regularizer that favors continuous and piecewise-linear functions with few affine ...

IEEE Computer Society2024

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, Lénaïc Chizat, Sebastian Jonas Neumayer

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, Stanislas Ducotterd, Pakshal Narendra Bohra, Alexis Marie Frederic Goujon, Sebastian Jonas Neumayer

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