arXiv subjects

Pierre-Antoine Thouvenin

Publications and source records attributed to Pierre-Antoine Thouvenin.

At least 19 recordsLinked to original sources

arXiv2026

A Hierarchical Likelihood Model for Non-linear Inverse Problems under Additive and Multiplicative Noise

Ill-posed inverse problems are encountered in numerous applications, possibly characterized by a highly non-linear forward model, both additive and multiplicative sources of noise, and censored data. In the absence of ground truth, uncertainty quantification is crucial to assess estimation reliability. This motivates the use of a Bayesian model and stochastic inference methods such as Markov Chain Monte Carlo algorithms. Problems combining all these challenges often lead to a complex and potentially multimodal posterior distribution, difficult to handle in practice. Approximate approaches have been proposed in the literature by either neglecting a source of noise or by using a tractable approximation of the likelihood function. These approaches either lead to an inaccurate model, or may require a complex calibration of the approximate likelihood. This paper proposes to tackle such problems with a general hierarchical Bayesian model and an efficient MCMC algorithm. The proposed formulation bypasses the need for calibrating the hyperparameters of an approximate model and is more versatile. The proposed method is assessed on a challenging scenario encountered in astronomy using synthetic data, in a variety of noise and censoring configurations. Comparisons are conducted against two baselines and a state-of-the-art method applicable in this context. The proposed approach is general and yields state-of-the-art results in terms of point-wise estimates and computing costs, with superior predictive performance. Results in the supplementary material further complete this comprehensive and rigorous model study. This work can serve as a guide for practitioners to select the best likelihood model according to their specific application.

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arXiv2026

Chemical diversity of dense cores in Orion B: The role of the environment

Prestellar cores are the sites of the earliest stages of star formation. Dust continuum observations are often used to identify and characterize their properties yet only a small fraction of them was observed and studied in terms of their composition and dynamical status. We explore the chemical diversity of prestellar cores and protostellar cores residing in the Orion B giant molecular cloud selected on their dust continuum emission to provide an unbiased view of their line emission properties and how they vary as function of the core parameters and environment. We make use of the large scale maps of Orion B in 25 molecular lines from which we extract information for a sample of 1001 cores selected using positions extracted from \textit{Herschel} dust continuum observations. The main properties of the core sample are derived using the Principal Component Analysis and additional maps of physical parameters: column density $N_{\rm{H_2}}$, far-ultraviolet (FUV) radiation field $G_0$ and mean volume gas density $n$. Additional high spectral resolution observations of $\rm C^{18}O(1-0)$ serve to evaluate the dynamical status of cores. The average line width of the cores is larger than what is typically expected for prestellar cores of closer star forming regions, which suggests that cores in Orion B are subjected to stronger turbulence affecting their stability. The first factor of the PCA analysis explaining the variation of the detected line intensities is the core column density of molecular gas. The second factor explains how the core chemical composition is strictly linked to their environment, which can be traced by the ratio of the external FUV radiation field over the core volume density, $G_0/n$. The third factor explaining the core chemical diversity is the mean density along the core line of sight, which is also associated with freeze-out and fractionation signatures.

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arXiv2026

A Distributed Plug-and-Play MCMC Algorithm for High-Dimensional Inverse Problems

Markov Chain Monte Carlo (MCMC) algorithms are standard approaches to solve imaging inverse problems and quantify estimation uncertainties, a key requirement in absence of ground-truth data. To improve estimation quality, Plug-and-Play MCMC algorithms, such as PnP-ULA, have been recently developed to accommodate priors encoded by a denoising neural network. Designing scalable samplers for high-dimensional imaging inverse problems remains a challenge: drawing and storing high-dimensional samples can be prohibitive, especially for high-resolution images. To address this issue, this work proposes a distributed sampler based on approximate data augmentation and PnP-ULA to solve very large problems. The proposed sampler uses lightweight denoising convolutional neural network, to efficiently exploit multiple GPUs on a Single Program Multiple Data architecture. Reconstruction performance and scalability are evaluated on several imaging problems. Communication and computation overheads due to the denoiser are carefully discussed. The proposed distributed approach noticeably combines three very precious qualities: it is scalable, enables uncertainty quantification, for a reconstruction performance comparable to other PnP methods.

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arXiv2025

Estimating the dense gas mass of molecular clouds using spatially unresolved 3 mm line observations

We aim to develop a new method to infer the sub-beam probability density function (PDF) of H2 column densities and the dense gas mass within molecular clouds using spatially unresolved observations of molecular emission lines in the 3 mm band. We model spatially unresolved line integrated intensity measurements as the average of an emission function weighted by the sub-beam column density PDF. The emission function, which expresses the line integrated intensity as a function of the gas column density, is an empirical fit to high resolution (< 0.05 pc) multi-line observations of the Orion B molecular cloud. The column density PDF is assumed to be parametric, composed of a lognormal distribution at moderate column densities and a power law distribution at higher column densities. To estimate the sub-beam column density PDF, the emission model is combined with a Bayesian inversion algorithm (the Beetroots code), which takes account of thermal noise and calibration errors. We validate our method by demonstrating that it recovers the true column density PDF of the Orion B cloud, reproducing the observed emission line integrated intensities. We apply the method to 12CO(J=1-0), 13CO(J=1-0), C18O(J=1-0), HCN(J=1-0), HCO+(J=1-0) and N2H+(J=1-0) observations of a 700 x 700 pc2 field of view (FoV) in the nearby galaxy M51. On average, the model reproduces the observed intensities within 30%. The column density PDFs obtained for the spiral arm region within our test FoV are dominated by a power-law tail at high column densities, with slopes that are consistent with gravitational collapse. Outside the spiral arm, the column density PDFs are predominantly lognormal, consistent with supersonic isothermal turbulence. We calculate the mass associated with the powerlaw tail of the column density PDFs and observe a strong, linear correlation between this mass and the 24$μ$m surface brightness.

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arXiv2025

Tracers of the ionization fraction in dense and translucent molecular gas: II. Using mm observations to constrain ionization fraction across Orion B

The ionization fraction ($f_\mathrm{e}=n_\mathrm{e}/n_\mathrm{H}$) is a crucial parameter of interstellar gas, yet estimating it requires deep knowledge of molecular gas chemistry and observations of specific lines, such as those from isotopologs like HCO$^+$ and N$_2$H$^+$, which are detectable only in dense cores. Previous challenges in constraining $f_\mathrm{e}$ over large areas stemmed from the limitations of observational tracers and chemical models. Recent models have identified molecular line ratios that can trace $f_\mathrm{e}$ in different environments within molecular clouds. In this study, we analyze various molecular lines in the 3-4 mm range to derive the ionization fraction across the Orion B giant molecular cloud. We focus on dense and translucent gas, exploring variations with gas density ($n$) and the far-ultraviolet (FUV) radiation field ($G_0$). Our findings show that the ionization fraction ranges from $10^{-5.5}$ to $10^{-4}$ in translucent gas and $10^{-8}$ to $10^{-6}$ in dense gas. Notably, $f_\mathrm{e}$ is sensitive to $G_0$ in dense, UV-illuminated regions, decreasing with increasing volume density ($f_\mathrm{e} \propto n^{-0.227}$ for dense and $f_\mathrm{e} \propto n^{-0.3}$ for translucent gas) and increasing with $G_0$. In translucent gas, differing line ratios yield consistent fe values, indicating the importance of electron excitation of HCN and HNC. For dense gas, we recommend using the CN(1-0)/N$_2$H$^+$(1-0) ratio for upper limits on fe and C$^{18}$O(1-0)/HCO$^+$(1-0) for lower limits. In translucent environments, CCH(1-0)/HNC(1-0) effectively traces $f_\mathrm{e}$. The higher fe values in translucent gas align with the C$^+$/CI/CO transition, while values in dense gas are adequate for coupling with the magnetic field.

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arXiv2025

Time and covariance smoothing for restoration of bivariate signals

In many applications and physical phenomena, bivariate signals are polarized, i.e. they trace an elliptical trajectory over time when viewed in the 2D planes of their two components. The smooth evolution of this elliptical trajectory, called polarization ellipse, is highly informative to solve ill-posed inverse problems involving bivariate signals where the signal is collected through indirect, noisy or incomplete measurements. This work proposes a novel formulation and an efficient algorithm for reconstructing bivariate signals with polarization regularization. The proposed formulation leverages the compact representation of polarization through the instantaneous covariance matrices. To address the resulting quartic optimization problem, we propose a well-suited parameter splitting strategy which leads to an efficient iterative algorithm (alternating direction method of multipliers (ADMM)) with convex subproblems at each iteration. The performance of the proposed method is illustrated on numerical synthetic data experiments.

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arXiv2025

Beetroots: spatially-regularized Bayesian inference of physical parameter maps -- Application to Orion

The current generation of millimeter receivers is able to produce cubes of 800 000 pixels by 200 000 frequency channels to cover several square degrees over the 3 mm atmospheric window. Estimating the physical conditions of the interstellar medium (ISM) with an astrophysical model on such datasets is challenging. Common approaches tend to converge to local minima and typically poorly reconstruct regions with low signal-to-noise ratio (S/N). This instrumental revolution thus calls for new scalable data analysis techniques. We present Beetroots, a Python software that performs Bayesian reconstruction of maps of physical conditions from observation maps and an astrophysical model. It relies on an accurate statistical model, exploits spatial regularization to guide estimations, and uses state-of-the-art algorithms. It also assesses the ability of the astrophysical model to explain the observations, providing feedback to improve ISM models. We demonstrate the power of Beetroots with the Meudon PDR code on synthetic data, and then apply it to estimate physical condition maps in the full Orion molecular cloud 1 (OMC-1) star forming region based on Herschel molecular line emission maps. The application to the synthetic case shows that Beetroots can currently analyse maps with up to ten thousand pixels, addressing large variations of S/N, escaping from local minima, and providing consistent uncertainty quantifications. On a laptop, the inference runtime ranges from a few minutes for 100-pixel maps to 28 hours for 8100-pixel maps. The results on the OMC-1 maps are consistent with independent estimations from the literature, and improve our understanding of the region. This work paves the way towards systematic and rigorous analyses of observations produced by current and future instruments.

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arXiv2025

Denoising bivariate signals via smoothing and polarization priors

We propose two formulations to leverage the geometric properties of bivariate signals for dealing with the denoising problem. In doing so, we use the instantaneous Stokes parameters to incorporate the polarization state of the signal. While the first formulation exploits the statistics of the Stokes representation in a Bayesian setting, the second uses a kernel regression formulation to impose locally smooth time-varying polarization properties. In turn, we obtain two formulations that allow us to use both signal and polarization domain regularization for denoising a bivariate signal. The solutions to them exploit the polarization information efficiently as demonstrated in the numerical simulations

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arXiv2024

Toward a robust physical and chemical characterization of heterogeneous lines of sight: The case of the Horsehead nebula

Dense cold molecular cores/filaments are surrounded by an envelope of translucent gas. Some of the low-J emission lines of CO and HCO$^+$ isotopologues are more sensitive to the conditions either in the translucent environment or in the dense cold one. We propose a cloud model composed of three homogeneous slabs of gas along each line of sight (LoS), representing an envelope and a shielded inner layer. IRAM-30m data from the ORION-B large program toward the Horsehead nebula are used to demonstrate the method's capability. We use the non-LTE radiative transfer code RADEX to model the line profiles from the kinetic temperature $T_{kin}$, the volume density $n_{H_2}$, kinematics and chemical properties of the different layers. We then use a maximum likelihood estimator to simultaneously fit the lines of the CO and HCO$^+$ isotopologues. We constrain column density ratios to limit the variance on the estimates. This simple heterogeneous model provides good fits of the fitted lines over a large part of the cloud. The decomposition of the intensity into three layers allows to discuss the distribution of the estimated physical/chemical properties along the LoS. About 80$\%$ the CO integrated intensity comes from the envelope, while $\sim55\%$ of that of the (1-0) and (2-1) lines of C$^{18}$O comes from the inner layer. The $N(^{13}CO)/N(C^{18}O)$ in the envelope increases with decreasing $A_v$, and reaches $25$ in the pillar outskirts. The envelope $T_{kin}$ varies from 25 to 40 K, that of the inner layer drops to $\sim 15$ K in the western dense core. The inner layer $n_{H_2}$ is $\sim 3\times10^4\,\text{cm}^{-3}$ toward the filament and it increases by a factor $10$ toward dense cores. The proposed method correctly retrieves the physical/chemical properties of the Horsehead nebula and offers promising prospects for less supervised model fits of wider-field datasets.

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arXiv2024

Quantifying the informativity of emission lines to infer physical conditions in giant molecular clouds. I. Application to model predictions

Observations of ionic, atomic, or molecular lines are performed to improve our understanding of the interstellar medium (ISM). However, the potential of a line to constrain the physical conditions of the ISM is difficult to assess quantitatively, because of the complexity of the ISM physics. The situation is even more complex when trying to assess which combinations of lines are the most useful. Therefore, observation campaigns usually try to observe as many lines as possible for as much time as possible. We search for a quantitative statistical criterion to evaluate the constraining power of a (or combination of) tracer(s) with respect to physical conditions in order to improve our understanding of the statistical relationships between ISM tracers and physical conditions and helps observers to motivate their observation proposals. The best tracers are obtained by comparing the mutual information between a physical parameter and different sets of lines. We apply this method to simulations of radio molecular lines emitted by a photodissociation region similar to the Horsehead Nebula that would be observed at the IRAM 30m telescope. We search for the best lines to constrain the visual extinction $A_v^{tot}$ or the far UV illumination $G_0$. The most informative lines change with the physical regime (e.g., cloud extinction). Short integration time of the CO isotopologue $J=1-0$ lines already yields much information on the total column density most regimes. The best set of lines to constrain the visual extinction does not necessarily combine the most informative individual lines. Precise constraints on $G_0$ are more difficult to achieve with molecular lines. They require spectral lines emitted at the cloud surface (e.g., [CII] and [CI] lines). This approach allows one to better explore the knowledge provided by ISM codes, and to guide future observation campaigns.

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arXiv2024

Bias versus variance when fitting multi-species molecular lines with a non-LTE radiative transfer model

Robust radiative transfer techniques are requisite for efficiently extracting the physical and chemical information from molecular rotational lines.We study several hypotheses that enable robust estimations of the column densities and physical conditions when fitting one or two transitions per molecular species. We study the extent to which simplifying assumptions aimed at reducing the complexity of the problem introduce estimation biases and how to detect them.We focus on the CO and HCO+ isotopologues and analyze maps of a 50 square arcminutes field. We used the RADEX escape probability model to solve the statistical equilibrium equations and compute the emerging line profiles, assuming that all species coexist. Depending on the considered set of species, we also fixed the abundance ratio between some species and explored different values. We proposed a maximum likelihood estimator to infer the physical conditions and considered the effect of both the thermal noise and calibration uncertainty. We analyzed any potential biases induced by model misspecifications by comparing the results on the actual data for several sets of species and confirmed with Monte Carlo simulations. The variance of the estimations and the efficiency of the estimator were studied based on the Cram{é}r-Rao lower bound.Column densities can be estimated with 30% accuracy, while the best estimations of the volume density are found to be within a factor of two. Under the chosen model framework, the peak 12CO(1--0) is useful for constraining the kinetic temperature. The thermal pressure is better and more robustly estimated than the volume density and kinetic temperature separately. Analyzing CO and HCO+ isotopologues and fitting the full line profile are recommended practices with respect to detecting possible biases.Combining a non-local thermodynamic equilibrium model with a rigorous analysis of the accuracy allows us to obtain an efficient estimator and identify where the model is misspecified. We note that other combinations of molecular lines could be studied in the future.

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arXiv2023

A Distributed Block-Split Gibbs Sampler with Hypergraph Structure for High-Dimensional Inverse Problems

Sampling-based algorithms are classical approaches to perform Bayesian inference in inverse problems. They provide estimators with the associated credibility intervals to quantify the uncertainty on the estimators. Although these methods hardly scale to high dimensional problems, they have recently been paired with optimization techniques, such as proximal and splitting approaches, to address this issue. Such approaches pave the way to distributed samplers, splitting computations to make inference more scalable and faster. We introduce a distributed Split Gibbs sampler (SGS) to efficiently solve such problems involving distributions with multiple smooth and non-smooth functions composed with linear operators. The proposed approach leverages a recent approximate augmentation technique reminiscent of primal-dual optimization methods. It is further combined with a block-coordinate approach to split the primal and dual variables into blocks, leading to a distributed block-coordinate SGS. The resulting algorithm exploits the hypergraph structure of the involved linear operators to efficiently distribute the variables over multiple workers under controlled communication costs. It accommodates several distributed architectures, such as the Single Program Multiple Data and client-server architectures. Experiments on a large image deblurring problem show the performance of the proposed approach to produce high quality estimates with credibility intervals in a small amount of time. Supplementary material to reproduce the experiments is available online.

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arXiv2023

Neural network-based emulation of interstellar medium models

The interpretation of observations of atomic and molecular tracers in the galactic and extragalactic interstellar medium (ISM) requires comparisons with state-of-the-art astrophysical models to infer some physical conditions. Usually, ISM models are too time-consuming for such inference procedures, as they call for numerous model evaluations. As a result, they are often replaced by an interpolation of a grid of precomputed models. We propose a new general method to derive faster, lighter, and more accurate approximations of the model from a grid of precomputed models. These emulators are defined with artificial neural networks (ANNs) designed and trained to address the specificities inherent in ISM models. Indeed, such models often predict many observables (e.g., line intensities) from just a few input physical parameters and can yield outliers due to numerical instabilities or physical bistabilities. We propose applying five strategies to address these characteristics: 1) an outlier removal procedure; 2) a clustering method that yields homogeneous subsets of lines that are simpler to predict with different ANNs; 3) a dimension reduction technique that enables to adequately size the network architecture; 4) the physical inputs are augmented with a polynomial transform to ease the learning of nonlinearities; and 5) a dense architecture to ease the learning of simple relations. We compare the proposed ANNs with standard classes of interpolation methods to emulate the Meudon PDR code, a representative ISM numerical model. Combinations of the proposed strategies outperform all interpolation methods by a factor of 2 on the average error, reaching 4.5% on the Meudon PDR code. These networks are also 1000 times faster than accurate interpolation methods and require ten to forty times less memory. This work will enable efficient inferences on wide-field multiline observations of the ISM.

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arXiv2023

Parallel faceted imaging in radio interferometry via proximal splitting (Faceted HyperSARA): I. Algorithm and simulations

Upcoming radio interferometers are aiming to image the sky at new levels of resolution and sensitivity, with wide-band image cubes reaching close to the Petabyte scale for SKA. Modern proximal optimization algorithms have shown a potential to significantly outperform CLEAN thanks to their ability to inject complex image models to regularize the inverse problem for image formation from visibility data. They were also shown to be parallelizable over large data volumes thanks to a splitting functionality enabling the decomposition of the data into blocks, for parallel processing of block-specific data-fidelity terms involved in the objective function. Focusing on intensity imaging, the splitting functionality is further exploited in this work to decompose the image cube into spatio-spectral facets, and enable parallel processing of facet-specific regularization terms in the objective function, leading to the "Faceted HyperSARA" algorithm. Reliable heuristics enabling an automatic setting of the regularization parameters involved in the objective are also introduced, based on estimates of the noise level, transferred from the visibility domain to the domains where the regularization is applied. Simulation results based on a MATLAB implementation and involving synthetic image cubes and data close to Gigabyte size confirm that faceting can provide a major increase in parallelization capability when compared to the non-faceted approach (HyperSARA).

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arXiv2023

Parallel faceted imaging in radio interferometry via proximal splitting (Faceted HyperSARA): II. Code and real data proof of concept

In a companion paper, a faceted wideband imaging technique for radio interferometry, dubbed Faceted HyperSARA, has been introduced and validated on synthetic data. Building on the recent HyperSARA approach, Faceted HyperSARA leverages the splitting functionality inherent to the underlying primal-dual forward-backward algorithm to decompose the image reconstruction over multiple spatio-spectral facets. The approach allows complex regularization to be injected into the imaging process while providing additional parallelization flexibility compared to HyperSARA. The present paper introduces new algorithm functionalities to address real datasets, implemented as part of a fully fledged MATLAB imaging library made available on Github. A large scale proof-of-concept is proposed to validate Faceted HyperSARA in a new data and parameter scale regime, compared to the state-of-the-art. The reconstruction of a 15 GB wideband image of Cyg A from 7.4 GB of VLA data is considered, utilizing 1440 CPU cores on a HPC system for about 9 hours. The conducted experiments illustrate the reconstruction performance of the proposed approach on real data, exploiting new functionalities to leverage known direction-dependent effects (DDEs), for an accurate model of the measurement operator, and an effective noise level accounting for imperfect calibration. They also demonstrate that, when combined with a further dimensionality reduction functionality, Faceted HyperSARA enables the recovery of a 3.6 GB image of Cyg A from the same data using only 91 CPU cores for 39 hours. In this setting, the proposed approach is shown to provide a superior reconstruction quality compared to the state-of-the-art wideband CLEAN-based algorithm of the WSClean software.

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arXiv2023

Deep learning denoising by dimension reduction: Application to the ORION-B line cubes

Context. The availability of large bandwidth receivers for millimeter radio telescopes allows the acquisition of position-position-frequency data cubes over a wide field of view and a broad frequency coverage. These cubes contain much information on the physical, chemical, and kinematical properties of the emitting gas. However, their large size coupled with inhomogenous signal-to-noise ratio (SNR) are major challenges for consistent analysis and interpretation.Aims. We search for a denoising method of the low SNR regions of the studied data cubes that would allow to recover the low SNR emission without distorting the signals with high SNR.Methods. We perform an in-depth data analysis of the 13 CO and C 17 O (1 -- 0) data cubes obtained as part of the ORION-B large program performed at the IRAM 30m telescope. We analyse the statistical properties of the noise and the evolution of the correlation of the signal in a given frequency channel with that of the adjacent channels. This allows us to propose significant improvements of typical autoassociative neural networks, often used to denoise hyperspectral Earth remote sensing data. Applying this method to the 13 CO (1 -- 0) cube, we compare the denoised data with those derived with the multiple Gaussian fitting algorithm ROHSA, considered as the state of the art procedure for data line cubes.Results. The nature of astronomical spectral data cubes is distinct from that of the hyperspectral data usually studied in the Earth remote sensing literature because the observed intensities become statistically independent beyond a short channel separation. This lack of redundancy in data has led us to adapt the method, notably by taking into account the sparsity of the signal along the spectral axis. The application of the proposed algorithm leads to an increase of the SNR in voxels with weak signal, while preserving the spectral shape of the data in high SNR voxels.Conclusions. The proposed algorithm that combines a detailed analysis of the noise statistics with an innovative autoencoder architecture is a promising path to denoise radio-astronomy line data cubes. In the future, exploring whether a better use of the spatial correlations of the noise may further improve the denoising performances seems a promising avenue. In addition,

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arXiv2023

Efficient sampling of non log-concave posterior distributions with mixture of noises

This paper focuses on a challenging class of inverse problems that is often encountered in applications. The forward model is a complex non-linear black-box, potentially non-injective, whose outputs cover multiple decades in amplitude. Observations are supposed to be simultaneously damaged by additive and multiplicative noises and censorship. As needed in many applications, the aim of this work is to provide uncertainty quantification on top of parameter estimates. The resulting log-likelihood is intractable and potentially non-log-concave. An adapted Bayesian approach is proposed to provide credibility intervals along with point estimates. An MCMC algorithm is proposed to deal with the multimodal posterior distribution, even in a situation where there is no global Lipschitz constant (or it is very large). It combines two kernels, namely an improved version of (Preconditioned Metropolis Adjusted Langevin) PMALA and a Multiple Try Metropolis (MTM) kernel. Whenever smooth, its gradient admits a Lipschitz constant too large to be exploited in the inference process. This sampler addresses all the challenges induced by the complex form of the likelihood. The proposed method is illustrated on classical test multimodal distributions as well as on a challenging and realistic inverse problem in astronomy.

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arXiv2018

Partially Asynchronous Distributed Unmixing of Hyperspectral Images

So far, the problem of unmixing large or multitemporal hyperspectral datasets has been specifically addressed in the remote sensing literature only by a few dedicated strategies. Among them, some attempts have been made within a distributed estimation framework, in particular relying on the alternating direction method of multipliers (ADMM). In this paper, we propose to study the interest of a partially asynchronous distributed unmixing procedure based on a recently proposed asynchronous algorithm. Under standard assumptions, the proposed algorithm inherits its convergence properties from recent contributions in non-convex optimization, while allowing the problem of interest to be efficiently addressed. Comparisons with a distributed synchronous counterpart of the proposed unmixing procedure allow its interest to be assessed on synthetic and real data. Besides, thanks to its genericity and flexibility, the procedure investigated in this work can be implemented to address various matrix factorization problems.

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