Research topics

My research focuses on the development and analysis of numerical methods for solving inverse problems and for high-dimensional learning. It is motivated by real-world applications in image and data processing.

It combines tools from optimization, harmonic analysis, inverse problems, statistical learning, and scientific computing.

My work is driven by the desire to cover the entire development pipeline for solving a problem: from physical modeling to applications on real-world data, through the design of the method, its theoretical analysis, and its implementation on highly parallel architectures.

Inverse problems in microscopy

Images from fluorescence microscopes are degraded by spatially varying blurs, and the operators that model them are huge: up to \(10^{18}\) entries for a 3D volume. We develop fast approximations of these operators (wavelet and product-convolution expansions) and methods to estimate them from calibration images. We also build low-dimensional models of whole families of microscope operators, and neural networks that identify the point spread function directly from the data.

JMIV 2017 ACHA 2017 IMA JNA 2020 IEEE TCI 2021 DeepInverse

Inverse problems in photoacoustic tomography

Photoacoustic tomography images optical absorption deep inside biological tissue with submillimeter resolution, by measuring the ultrasound waves generated by a laser pulse. Achieving high-quality reconstruction requires modeling the spatially varying impulse response of the detectors, which leads to operators that are hundreds of terabytes in size. We develop scalable GPU implementations of these operators based on the Green's function of the wave equation. We also work on fast non-convex reconstruction algorithms and on the calibration of the acquisition system.

Preprint GRETSI 2025 PATminton

Concentration of the minimizers of empirical risks

Machine learning models, from linear regression to deep neural networks, are trained by empirical risk minimization: we minimize the average loss over a finite set of samples as a proxy for the true (population) risk, which is unknown. Learning theory usually bounds the excess risk. In many problems, however, what matters is how close the minimizers of the empirical risk are to those of the population risk. We proposed a general framework, based on the local geometry of the risk around its minimizers, that gives optimal concentration rates for a broad class of problems.

JMLR 2024

People

Postdocs

• Florian Sarron (2026–2027), with P. Weiss

PhD students

• Romain Bonnet-Eymard (2025–), with R. Bouclier
  Image correlation based on physics-informed neural networks for the identification of mechanical property fields

• Trung-Thai Do (2024–), with C. Chaux
  Large-scale reconstruction methods for high-quality 3D photoacoustic imaging

• Camille Ferrassou (2023–), with R. Bouclier, M. Duval and L. Risser
  Construction of digital twins of military aircraft using robust machine learning techniques for monitoring mechanical aging

Master 2

• Siyuan Li (2026), with B. Charlier
  Dimensionality reduction for spatial omics data analysis

• Soa Durand (2026), with M. Costa and J. Fehrenbach
  Transformation of a fluorescence-time signal into a DNA concentration-size distribution

• Iyad Zekhnini (2025), with F. Iutzeler
  Concentration of the geometry of empirical risks

• Maxime Lafont (2021), with C. Chaux and J. Gateau
  A numerical method for fast 3D photoacoustic tomography with arbitrary geometry of sensors

Master 1

• Hoai-Viet Dang (2026), with E. Soubies
  Computational imaging with simple lenses

• Trung-Thai Do (2023)
  Reconstruction methods for photoacoustic imaging

• Tiphaine Vaisson (2023)
  Calibration of product-convolution operators

• Minh Hai Nguyen (2022), with P. Weiss
  Product-convolution neural networks

• Mamadou Oury-Bah (2022)
  Reconstruction methods for photoacoustic imaging

Funding

Ongoing

• SO-LAR (2027–2030) ANR PRME, PI: P. Escande
  SO – Landscape analysis of risks

• CLEAR-MICROSCOPY (2026–2030) ANR PRC, PI: P. Weiss, co-PI: P. Escande
  Computational Learning for Efficient and Accurate Reconstruction in Microscopy

• CRIPI (2025–2027) LabEx CIMI, PI: P. Escande
  Calibration and Reconstruction methods for Inverse Problems in Imaging

• LASCAR-3D (2025–2026) CNRS MITI, PI: P. Escande
  Large-scale reconstruction methods for high-quality 3D biomedical photoacoustic imaging

Past

• MICROBLIND (2021–2025) ANR PRC, PI: P. Weiss
  Blind inverse problems and optical microscopy

• EROSION (2022–2025) ANR JCJC, PI: E. Soubies
  Exact RelaxatiOns for Sparse and low-rank optImizatiON

• COCON 3D (2021–2022) France Life Imaging, PI: P. Escande
  Co-conception of fast tomographic approaches for high-quality 3D photoacoustic imaging

• SPLIN (2021–2022) GdR ISIS, PI: L. Calatroni
  SParse & non-convex optimisation approaches for data-adaptive Learning of INverse image microscopy problems