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, Jonathan Yuelin Dong, Pol del Aguila Pla

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, Alexis Marie Frederic Goujon, Stanislas Ducotterd

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, Sebastian Jonas Neumayer, Stanislas Ducotterd

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