The study of aerosol plumes emitted by industrial sites (e.g. steelworks and oil refineries) into the atmosphere is a public health issue and a matter of concern for controlling pollutant emissions. Optical spectral imaging remote sensing, such as that provided by Sentinel-2 (ESA), enables regular, large-scale monitoring over time. Furthermore, the recent launches of the PRISMA and ENMAP hyperspectral satellites [1] and the upcoming launches of satellites such as CHIME (ESA) and BIODIVERSITY (CNES) provide access to rich spectral information with high spatial resolution. While these tools are primarily intended for studying continental surfaces, recent studies have demonstrated that hyperspectral satellite imaging can be employed to monitor ‘hot spots’ of major sources of atmospheric pollutant emissions, particularly with respect to particulate matter. However, the main limitation of current methods for characterising aerosol plumes is that jointly estimating the optical properties of the ground beneath the plume and the plume's characteristics is an underdetermined inverse problem [1]. Previous work at ONERA estimates the reflectance beneath the plume using a multi-spectral image (or time series) acquired without the plume at a date close to that of the hyperspectral image to constrain the problem [1].  These methods use CNMF (coupled non-negative matrix factorisation) matrix decomposition, which is based on two assumptions about the optical properties of soils: i) each pixel is a linear combination of a set of characteristic pixels from the hyperspectral image itself (known as 'end-member' pixels); and ii) it is possible to find a plume-free multi spectral image acquired during a close time interval, during which the soil structure is assumed to be stable.

The aim of the thesis is to overcome the current limitations imposed by these simplifying assumptions by developing a method for jointly inverting the properties of the plume and the surface reflectance while eliminating the need for a ‘plume-free’ image. To this end, the doctoral student will study how statistical generative models [2] (e.g. variational autoencoders (VAEs)) can constrain the problem by providing prior information on surface reflectance beneath the plume.

Preliminary work, carried out as part of a collaborative research internship between CNES and ONERA, has demonstrated the potential of VAEs for regularizing the inverse problem. In particular, it has been shown that using a VAE to approximate the probability distribution of reflectance spectra allows:

-    to better estimate surface reflectance in the presence of plume when reflectance is not a linear combination of the image's end-members,

-    to eliminate the need to use a plume-free image acquired close to the date of the hyperspectral image.

The primary objective of the thesis is to consolidate and extend the results of the internship, which serve as proof of concept. In particular, the doctoral student will conduct further numerical experiments, both on simulated and real data, and on more plume parameters.

The second objective of the thesis is to develop a method for providing uncertainties with the inversion result. In previous PhD theses carried out at ONERA, the covariance matrix of reconstruction errors in the CNMF method is used to calculate the uncertainty associated with the reflectance estimate. However, these uncertainties are estimated on reconstructions outside the plume and do not always reflect the errors or biases in reconstruction within the plume. Here, we draw inspiration from the work of Biquard et al. [3] to reformulate the inversion problem as the estimation of the posterior distribution of plume parameters and surface reflectance, rather than as a maximum a posteriori problem, which results in a point estimate of the parameters.

The third objective of the thesis is to integrate the information provided by multispectral images taken close to the date of acquisition of the hyperspectral image in order to: i) better condition the reflectances of an image at time t by also relying on the images closest in time, and ii) ensure more detailed temporal monitoring of industrial effluents. 

 [1] Calassou, G., Foucher, P.-Y., and Léon, J.-F.: Quantifying particulate matter optical properties and flow rate in industrial stack plumes from the PRISMA hyperspectral imager, At-mos. Meas. Tech., 17, 57–71, https://doi.org/10.5194/amt-17-57-2024, 2024.

 [2] Kingma, D. P., & Welling, M. (2013). Auto-encoding variational bayes. In Proceedings of the International Conference on Learning Representations (ICLR), 2014.

[3] Biquard, M., Chabert, M., Genin, F., Latry, C., & Oberlin, T. (2025). Variational Bayes image restoration with compressive autoencoders. IEEE Transactions on Image Processing.

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For more Information about the topics and the co-financial partner (found by the lab!); contact Directeur de thèse - pierre-yves.foucher@onera.fr

Then, prepare a resume, a recent transcript and a reference letter from your M2 supervisor/ engineering school director and you will be ready to apply online before March 13th, 2026 Midnight Paris time!