publications

2025

1. 

   Sketchpose: Learning to Segment Cells with Partial Annotations

   Clément Cazorla, Nathanaël Munier, Renaud Morin, and 1 more author

   In , 2025

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   The most popular networks used for cell segmentation (e.g. Cellpose, Stardist, HoverNet,...) rely on a prediction of a distance map. It yields unprecedented accuracy but hinges on fully annotated datasets. This is a serious limitation to generate training sets and perform transfer learning. In this paper, we propose a method that still relies on the distance map and handles partially annotated objects. We evaluate the performance of the proposed approach in the contexts of frugal learning, transfer learning and regular learning on regular databases. Our experiments show that it can lead to substantial savings in time and resources without sacrificing segmentation quality. The proposed algorithm is embedded in a user-friendly Napari plugin.

2. 

   Jackpot 2.0 : variété d’incertitude pour les problèmes inverses

   Nathanaël Munier, Emmanuel Soubies, and Pierre Weiss

   In XXXème Colloque Francophone de Traitement du Signal et des Images (GRETSI 2025), Aug 2025

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   Dans le contexte des problèmes inverses, nous avions introduit Jackpot 1.0, une méthode d’approximation de la région d’incertitude par une variété de dimension inférieure. Nous présentons une nouvelle méthode similaire qui détermine les points extrémaux des lignes de niveau de l’écart au modèle. Cette nouvelle méthode a deux avantages : elle repose uniquement sur un problème d’optimisation non contraint et elle renvoie des points qui maximisent le rapport entre écart de paramètre et écart de mesure. Cette méthode a été testée sur deux applications numériques de biologie des systèmes.

2024

1. 

   Jackpot: Approximating Uncertainty Domains with Adversarial Manifolds

   Nathanaël Munier, Emmanuel Soubies, and Pierre Weiss

   In , Aug 2024

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   Given a forward mapping Φ : RN → RM , the region x ∈ RN , ∥Φ(x) − y∥2 ≤ ε, where y ∈ RM is a given vector and ε ≥ 0 is a perturbation am- plitude, represents the set of all possible inputs x that could have produced the measurement y within an acceptable error margin. This set reflects the inherent uncertainty or indeterminacy in recovering the true input x solely from the noisy observation y, which is a key challenge in inverse problems. In this work, we develop a numerical algorithm called Jackpot (Jacobian Kernel Projection Optimization) which approximates this set with a low-dimensional adversarial manifold. The proposed algorithm leverages automatic differentation, allowing it to handle complex, high dimensional mappings such as those found when dealing with dynamical systems or neural networks. We demonstrate the effectiveness of our al- gorithm on various challenging large-scale, non-linear problems including parameter identification in dynamical systems and blind image deblurring. The algorithm is integrated within the Python package deepinv.

2. 

   Exploring instabilities of inverse problem solvers with low-dimensional manifolds

   Nathanaël Munier, Emmanuel Soubies, and Pierre Weiss

   Oct 2024

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   Inverse problem solvers are mappings S : Y → X , where Y is the space of measurements and X the space of signals we wish to recover. We propose a simple algorithm to visualize the main instability of a solver implemented within an automatic differentiation framework. We justify it through simple considerations and illustrate its behavior on a deconvolution problem solved with a neural network based reconstruction method. The proposed algorithm can be used to provide addi- tional insights on the properties of inverse problem solvers, and can be viewed as a simple uncertainty quantification technique.

2023

1. 

   The MLE is a reliable source: sharp performance guarantees for localization problems

   Nathanaël Munier, Emmanuel Soubies, and Pierre Weiss

   Inverse Problems, Nov 2023

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   Single source localization from low-pass filtered measurements is ubiquitous in optics, wireless communications and sound processing. We analyze the performance of the maximum likelihood estimator (MLE) in this context with additive white Gaussian noise. We derive necessary conditions and sufficient conditions on the maximum admissible noise level to reach a given precision with high probability. The two conditions match closely, with a discrepancy related to the conditioning of a noiseless cost function. They tightly surround the Cramér–Rao lower bound for low noise levels. However, they are significantly more precise to describe the performance of the MLE for larger levels. As an outcome, we obtain a new criterion for the design of point spread functions in single molecule microscopy.

2. 

   Sandpile groups of supersingular isogeny graphs

   Nathanaël MUNIER, and Ari SHNIDMAN

   Journal de Théorie des Nombres de Bordeaux, Nov 2023

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   Let p and q be distinct primes, and let Xp,q be the (q + 1)- regular graph whose nodes are supersingular elliptic curves over Fp and whose edges are q-isogenies. For fixed p, we compute the distribution of the ℓ-Sylow subgroup of the sandpile group (i.e. Jacobian) of Xp,q as q → ∞. We find that the distribution disagrees with the Cohen–Lenstra heuristic in this context. Our proof is via Galois representations attached to modular curves. As a corollary, we give an upper bound on the probability that the Jacobian is cyclic, which we conjecture to be sharp.

3. 

   Algorithmes de visualisation de non-identifiabilité

   Nathanaël Munier, Emmanuel Soubies, and Pierre Weiss

   In XXIXème Colloque Francophone de Traitement du Signal et des Images (GRETSI 2023), Aug 2023

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   The identification of a set of parameters x from observed data y is often reduced to the resolution of a problem of the type Φ(x) = y, where Φ is a continuous application. This equation appears in domains such as (blind) inverse problems, data assimilation, or optimal control. When the solution is not unique, it may be important to inform the user about the set of plausible solutions. We propose here an algorithm to locally describe a set of solutions of this equation. It is essentially based on automatic differentiation and on a local parameterization of the solution manifold. We illustrate the interest of this approach on two toy examples.