Réunion

9h00-9h30: Welcome

9h30-9h40: Introduction

9h40-10h30: Keynote. Julien Stoehr (CEREMADE, Paris) - Entropic Mirror Monte Carlo

Abstract. Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions in high dimensional spaces, the efficiency of importance sampling critically depends on the choice of the proposal distribution. In this paper, we propose a novel adaptive scheme for the construction of efficient proposal distributions. Our algorithm promotes efficient exploration of the target distribution by combining global sampling mechanisms with a delayed weighting procedure. The proposed weighting mechanism plays a key role by enabling rapid resampling in regions where the proposal distribution is poorly adapted to the target. Our sampling algorithm is shown to be geometrically convergent under mild assumptions and is illustrated through various numerical experiments.

This talk is based on the paper Entropic Mirror Monte Carlo (https://arxiv.org/abs/2602.03165). It is a joint work with Anas Cherradi, Yazid Janati, Alain Durmus, Sylvain Le Corff and Yohan Petetin.

10h50-11h10: Florent Leclercq (IAP, Paris): Counterfactual-informed adaptive MCMC with conditional normalising flows

Abstract. Markov Chain Monte Carlo (MCMC) methods are particularly robust because the Metropolis–Hastings (MH) acceptance test corrects for proposal inaccuracies, providing an asymptotic guarantee of convergence to the target distribution. A key ingredient is the proposal distribution, which determines sampling efficiency. However, theory offers no general prescription for designing such a proposal distribution. In high-dimensional settings, one often finds that any naïve proposal yields no accepted samples which could be used as training data. Moreover, if the data model is non-differentiable, gradients are also unavailable as training data. We address the automatic design of a proposal distribution in scenarios where naïve choices result in near-zero acceptance rates and gradients cannot be employed. Specifically, we consider models comprising a signal (an arbitrary, non-differentiable function of the parameters) and additive Gaussian noise. We present a geometric interpretation of the MH test in this context, showing that each test defines a hyperplane that partitions data space into acceptance and rejection regions. We demonstrate that a rejection in the MCMC of interest would correspond to an acceptance in an alternative chain if the true data vector were replaced by a suitably chosen alternative data vector, close in the Mahalanobis sense. Building on this insight, we introduce a novel MCMC algorithm that augments traditional MH sampling with “reasoning with counterfactuals.” By recording not only {accepted parameter, true data} pairs, but also {rejected parameter, alternative data} pairs that would have led to acceptance, we construct a replay buffer for training a conditional normalising flow. This normalising flow serves as an independence proposal alongside a vanilla random-walk proposal. The result is a general-purpose, adaptive MCMC method with a proposal distribution that self-improves by learning from both accepted and rejected moves. We evaluate the performance of our algorithm on challenging Bayesian inference tasks, including field-level inference in cosmological data analysis.

11h10-11h30: Mehdi Chahine Amrouche (Wheere & IRAP, Toulouse) - Efficient Sampling of Bernoulli-Gaussian-Mixtures for Sparse Signal Restoration

Abstract. In Bayesian inverse problems, sparse signal restoration frequently relies on hierarchical priors. The standard Bernoulli-Gaussian (BG) model is highly popular in this context, in particular because the Gaussian assumption on non-zero variables enables the use of highly efficient Markov Chain Monte Carlo (MCMC) methods, namely the Partially Collapsed Gibbs Sampler (PCGS). However, real-world signals often exhibit behaviors that BG cannot capture, requiring non-symmetric and/or heavy-tailed priors like the Bernoulli-Exponential (for non-negativity) or Bernoulli-Laplace models. Unfortunately, shifting to these non-Gaussian priors precludes the use of PCGS, leading to severe computational bottlenecks. To overcome this fundamental trade-off between modeling flexibility and algorithmic efficiency, this presentation explores the use of Bernoulli-Gaussian-Mixture (BGM) models. By modeling the non-zero variables of the signal as a Location-Scale Mixture of Gaussians (LSMG), the BGM framework can flexibly capture a wide variety of heavy-tailed and asymmetric distributions. Crucially, because the model decomposes into conditional Gaussians, it seamlessly restores the applicability of the PCGS algorithm. This work demonstrates how the BGM approach allows practitioners to tackle complex inverse problems—such as those enforcing non-negativity or heavy-tailed constraints—without sacrificing the computational speed and scalability associated with standard Gaussian priors.

11h30-11h50: Pierre Minier (IMS, Bordeaux) - Scalable Gibbs Sampling for Positive Image Deconvolution via Circulant Structures

Abstract: We address the problem of image deconvolution under positivity constraints with a focus on scalable inference and uncertainty quantification within a Bayesian framework. Such inverse problems typically involve a high-dimensional image, an informative or structural prior encoding constraints such as positivity and regularity, and unknown hyperparameters, including noise levels and possibly instrument-related parameters. To address these challenges, we propose an efficient Gibbs sampling strategy that exploits the circulant structure of the convolution operator. This structure enables fast updates of the image without relying on repeated FFT operations, while maintaining exact sampling steps. The proposed approach focuses on scalable sampling of the high-dimensional image, while hyperparameters are estimated using complementary and well-established techniques. In addition to point estimates, the proposed approach provides a full characterization of posterior uncertainties, including pixel-wise uncertainty maps and uncertainty on hyperparameters. We further justify this Gibbs strategy by comparing it with full-image samplers such as Langevin and Hamiltonian-based approaches, highlighting improved convergence behavior in the context of circulant image models. This results in a scalable inference scheme illustrated on imaging problems.

11h50-12h10: Jean-François Giovannelli (IMS, Bordeaux) - Deconvolution, diffusion prior, posterior sampling: Estimation of observational parameters

Abstract: This talk addresses the issue of inversion in cases where (1) the observation system is modeled by a linear transformation and additive noise, (2) the problem is ill-posed and regularization is introduced in a Bayesian framework, and (3) the prior density is modeled by a diffusion process adjusted on an available large set of examples.

• In this context, the issue of posterior sampling is well-known to be challenging, and we introduce a Gibbs algorithm called G-DSP (Gibbs Diffusion Posterior Sampler). This avenue appears to have been unexplored until now, and we demonstrate that this approach is both effective and remarkably simple. Furthermore, it exhibits some convergence properties in a clearly defined situation.
• The G-DSP opens a remarkable flexibility when it comes to estimating observation parameters (response and error parameters): it enables the re-use some standard approaches based on full-Bayes methodology and sampling algorithms. This second algorithm, an extension of the previous one, is referred to as Hyper-G-DSP

The talk will give several numerical experiments that clearly confirm the computational efficiency and the quality of both estimates and uncertainty quantification, for images and observation parameters.

* J.-F. Giovannelli, "A Gibbs posterior sampler for inverse problem based on prior diffusion model",https://arxiv.org/abs/2602.11711, EUSIPCO 2026

* J.-F. Giovannelli, "Estimation of instrument and noise parameters for inverse problem based on prior diffusion model", https://arxiv.org/abs/2602.11711, ICIP 2026

13h30-14h00: Poster session.

Clément Fernandes (Télécom SudParis) - Pairwise and Triplet Markov models in filtering and segmentation

Abstract. Hidden Markov chains are widely used in many fields such as speech and image processing, genome analysis, and prediction in economics, finance and meteorology. They enable the rapid processing of large amounts of data with minimal computing resources, while being particularly robust and, despite their simplicity, sufficiently effective in many situations. They have been extended to pairwise and triplet Markov chains, which can be useful for modeling more complex situations while maintaining the low complexity of the associated processing. The aim of this presentation will be to demonstrate the value of these extensions by presenting two situations in which they have proven relevant. The first situation deals with time series filtering when the noise is corelated and the hidden process is not necessarily Markovian. We will study the deterioration of the filter in the particular situation where the true Gaussian homogeneous Pairwise Markov chain model is replaced by the classical Hidden Markov chain model. We will illustrate this result with the real-life problem of estimating soil moisture by filtering the temperature sequence, showing that the Pairwise Markov chain model is better suited to the data than the Hidden one. The second situation is Bayesian unsupervised segmentation when the sojourn time in hidden states is not geometric, or when the data distribution is not stationary. In these cases, particular triplet Markov chains such as hidden semi-Markov chains and hidden evidential Markov chains tend to perform better than hidden Markov chains while preserving the ability to estimate the parameters with the Expectation Maximization algorithm. We will illustrate this point with some segmentations of synthetic images.

Nicolas Goeman (CRIStAL, Lille) - A hierarchical likelihood model for non-linear inverse problems under additive and multiplicative noises

Abstract. Inverse problems in astronomy presents many challenges related to the complexity of the physical models and sensitivity of acquisition devices. Data is typically perturbed by both additive and multiplicative noise sources and often censored. Considering both sources of noise is essential when the forward model is highly non-linear, with a dynamic range spanning several orders of magnitude. Finally, the quantification of uncertainties is crucial for scientific applications that aim to arbitrate between several hypotheses or models.

  The presence of two noise sources leads to a non-standard likelihood distribution, which makes the whole posterior difficult to sample efficiently using off-the-shelf algorithms. The approach proposed in (PALUD et al. 2023) takes into account all the challenges mentioned while still considering both noise sources. In this approach, a smooth interpolation between two likelihood approximations is considered. In the low amplitude regime, where the additive noise dominates, a purely additive approximation is used while in the high amplitude regime a purely multiplicative approximation is used since the multiplicative noise dominates. The transition in between these two extreme regimes is guided by some weight function. However, this interpolation suffers from an intractable normalization constant and introduces multiple hyperparameters that are difficult and costly to calibrate. 

  We propose an alternative to (PALUD et al. 2023), based on a hierarchical likelihood model. This approach does not require hyperparameter calibration, which makes it easier for practitioners to use and adaps to a wider range of problems. Furthermore, the two-level likelihood makes it possible to separate the forward model from the combination of two noise sources, thereby simplifying the sampling algorithm.

Elena Grosso (CNAM, Paris) - Spatio-temporal InSAR phase denoising with ADMM

Abstract. Interferometric Synthetic Aperture Radar (InSAR) is a remote sensing technique used to measure ground deformation by analysing the phase difference between two SAR images acquired over the same area. Multi-temporal InSAR (MT-InSAR) methods extend this approach by exploiting a time series of interferometric SAR images, allowing for improved accuracy and robustness through the integration of temporal information. In this context, Interferometric Phase Linking (IPL) is a technique used to denoise the phase of SAR images by exploiting the temporal information of all possible pairs of interferogram within the time series. Existing methods from the state of the art have mostly focused on maximum-likelihood and least-squares fitting formulations. We reformulated the task as a covariance matrix fitting problem (COFI), where the aim is to recover the expected InSAR phase structure from a noisy estimate of the covariance matrix of a pixel patch. SAR imagery intrinsically exhibits local statistical homogeneity; moreover, atmospheric effects induce spatially correlated phase variations across the image, providing valuable spatial statistical information. We have hence started working on adding a spatial regularisation term to the optimisation using is a 2-dimensional Total Variation (TV) methodology. The IPL problem requires the construction of a covariance matrix estimation that yields the temporal correlation between the phases and thus is not a simple and explicit function of the samples. The use of a spatial regularisation penalty term creates a strong interdependence between solutions and hence low scalability. To overcome this difficulty, we introduce a splitting variable approach, subject to an equality constraint in the optimization problem. This reformulation enables the use of the Alternating Direction Method of Multipliers (ADMM), thereby decomposing the problem into more tractable subproblems.

Raphael Schirru (SAFRAN) - Adaptive Bayesian Filtering with Reinforcement Learning for State Estimation against Abrupt Events, Model Mismatch and Low Observability

Abstract. The motivation of this work comes from the engine performance’s inverse problem, which consists of estimating latent health indicators (e.g., efficiencies, flow capacities) from operational flight measurements through the use of a forward thermodynamic model. Several major challenges arise from this problem: (i) model mismatch, no strong a priori is available on the true process dynamics, (ii) abrupt events, during its life, engine components can experience abrupt changes in health states caused by uninformed maintenance or unknown external events, and (iii) underdetermined setting, the number of available measurements is smaller than the number of latent health parameters. When poor a priori knowledge on the process dynamics is combined with underdetermination, the estimation problem becomes non-observable. This work reframes adaptive Kalman filtering as a sequential decision-making problem, where the agent learns to reshape either the process uncertainty or the dynamical structure itself in order to compensate for model mismatch, abrupt events, and structural non-observability

14h00-14h50: Keynote. Mame Diarra Fall (Université de Rouen Normandie) - Bayesian Approaches to Inverse Problems with deep learning-based priors

Abstract. Inverse problems are ubiquitous in signal and image processing. As inverse problems are known to be ill-posed or, at least, ill-conditioned, they require regularization through the introduction of additional constraints to mitigate the lack of information provided by the observations. A common difficulty lies in selecting an appropriate regularizer, which has a decisive influence on the quality of the reconstruction. Another challenge concerns the level of confidence we may have in the reconstructed signal or image. In other words, it is desirable for a method to quantify the uncertainty associated with the reconstructed image in order to promote more principled decision-making.

These two tasks - regularization and uncertainty quantification - can be addressed simultaneously within the Bayesian statistical framework. This approach makes it possible to incorporate additional information by specifying a marginal distribution for the image, known as the prior distribution. The traditional approach consists in defining the prior analytically, as a hand-crafted explicit function chosen to promote specific desired properties of the recovered image. Following the recent surge in deep learning, data-driven regularization using priors specified by neural networks has become widespread in image inverse problems. Popular approaches within this framework include Plug-and-Play (PnP) [1] and Regularization by Denoising (RED) [2].

In the first part of the talk, I will present the probabilistic approach to the RED framework we have introduced in [3], which defines a new probability distribution based on a RED potential that can be used as the prior distribution in a Bayesian inversion task. We also propose a dedicated Markov chain Monte Carlo (MCMC) sampling algorithm that is particularly well suited for high-dimensional sampling of the resulting posterior distribution. In addition, we provide a theoretical analysis guaranteeing convergence to the target distribution and quantifying the convergence rate. The effectiveness of the proposed approach is illustrated on various linear inverse restoration tasks such as image deblurring, inpainting, and super-resolution.

The second part of the talk will be devoted to a novel approach we proposed in [4], for solving Poisson inverse problems. We also develop a Monte Carlo sampling algorithm that accounts for the underlying non-Euclidean geometry of the problem. The proposed approach has been evaluated on different tasks such as denoising, deblurring, and positron emission tomography (PET) reconstruction.

References:

1. S. V. Venkatakrishnan et al. « Plug-and-Play priors for model based reconstruction ». In IEEE Global Conf. on Signal and Information Processing, pp 945-948, 2013.
2. Y. Romano, M. Elad and P. Milanfar, « The little engine that could: Regularization by denoising (RED), » SIAM Journal on Imaging Sciences, 10(4):1804–1844, 2017
3. E.C. Faye, M.D. Fall and N. Dobigeon. « Regularization by denoising: Bayesian model and Langevin-within-split Gibbs sampling », IEEE Transactions on Image Processing, vol 34, pages 221-234, 2024 
4. E.C. Faye, M.D. Fall, N. Dobigeon and É. Barat « Bregman geometry-aware split Gibbs sampling for Bayesian Poisson inverse problems », Submitted.

15h10-15h30: Clémentine Phung-Ngoc (LaTIM, Brest) - CT-free PET Reconstruction using Diffusion Models

Abstract. Attenuation correction (AC) is necessary for accurate activity quantification in positron emission tomography (PET). Conventional methods rely on attenuation maps derived from anatomical imaging, such as co-registered computed tomography (CT) or magnetic resonance (MR) scan. However, this approach suffers from several limitations, including increased radiation dose for the patient and possible mismatch artifacts. Here, we propose a new diffusion model (DM)-based joint reconstruction of activity and attenuation (JRAA) approach that relies solely on emission data, without anatomical imaging.

15h30-15h50: Barbara Pascal (LS2N, Nantes) - A Scaled Poisson Bayesian Model for Viral Epidemics monitoring

Abstract. Monitoring an ongoing epidemic requires accurate, trustworthy and easy to use tools. One of the most popular indicator to quantify a pathogen transmissibility over time is the effective reproduction number, defined as the expected number of secondary infections stemming from one typical individual infected at a given time. However, standard tools from epidemiology struggle to estimate it accurately from highly corrupted infection counts, such as those collected during COVID-19 pandemic. This presentation will first extend state-of-the-art epidemiological models for viral epidemics by introducing a scaled Poisson model, allowing to account for large intrinsic variability of infection counts during a real epidemic. Then, the associated scaled likelihood will be plugged into a Bayesian model with a quasi-noninformative prior. A carefully designed Markov Chain Monte Carlo algorithm, producing both a point estimate and credibility intervals of the reproduction number, will be presented in detail. Finally the accuracy and robustness to model misspecification and to scale parameter selection of the proposed estimator will be demonstrated through intensive numerical experiments on COVID-19 case counts in different countries and during various phases of the pandemic.

15h50-16h10: Tom Sprunck (CEA Saclay) - Bayesian model selection and misspecification testing in imaging inverse problems only from noisy and partial measurements

Abstract. Modern imaging techniques heavily rely on Bayesian statistical models to address difficult image reconstruction and restoration tasks. This paper addresses the objective evaluation of such models in settings where ground truth is unavailable, with a focus on model selection and misspecification diagnosis. Existing unsupervised model evaluation methods are often unsuitable for computational imaging due to their high computational cost and incompatibility with modern image priors defined implicitly via machine learning models. We herein propose a general methodology for unsupervised model selection and misspecification detection in Bayesian imaging sciences, based on a novel combination of Bayesian cross-validation and data fission, a randomized measurement splitting technique. The approach is compatible with any Bayesian imaging sampler, including diffusion and plug-and-play samplers. We demonstrate the methodology through experiments involving various scoring rules and types of model misspecification, where we achieve excellent selection and detection accuracy with a low computational cost.