Description du sujet de thèse

Context
Unsupervised learning algorithms, particularly segmentation or factorisation algorithms, can play a central role in the exploitation of spectral images in which each pixel is characterised by a complete spectrum. The use of X-ray spectroscopy makes it possible to characterise the elemental composition of each pixel, and measuring instruments can now collect images of several million pixels corresponding to several GB or even tens of GB. The wealth of information thus collected is useful, for example, for characterising highly complex and heterogeneous materials, such as those encountered in the study of ancient materials. However, this wealth of information calls for the development of analysis algorithms that are efficient in terms of computational cost, where standard segmentation algorithms are sub-optimal, both in terms of computational cost and in terms of exploiting prior knowledge about the data. We have already proposed an algorithm for segmenting X-ray fluorescence (XRF) spectral images, which combines bottom-up hierarchical classification and spatial constraints. This initial work uses χ2 distance as the aggregation criterion. In a second step, we used the likelihood loss criterion associated with the transition from a saturated model to a model of spectral homogeneity. These methodological results demonstrate that a statistically rigorous approach can reduce the number of photons needed to characterise each pixel of the material by a factor of between 100 and 1000, thereby reducing both the measurement time and the risk of radiation damage. Indirectly, this opens up the possibility of studying more samples, including more fragile ones

Objectives of the PhD
The theoretical results that form the basis of this work consider a model in which measurement uncertainty arises solely from the stochastic measurement process. Thus, for the time being, the proofs have only been verified for a specific noise distribution model, namely Poisson noise. This model is incomplete from the point of view of the actual complexity of ancient materials (archaeology, palaeontology, cultural heritage, etc.), and although these initial models already yield very promising results on both synthetic and real data, extending and generalising the theoretical results would allow them to be applied to other observation methods and modelling issues. The aim of the thesis is therefore to:
— With regard to measurement noise modelling, the XRF signals currently used follow a Poisson distribution. This is not the case for all modalities used on synchrotrons, and it will therefore be necessary to finely model the measurement noise of other modalities such as photoluminescence, infrared imaging, X-ray absorption, etc.
— Generalise the theoretical results concerning the properties of the likelihood loss criterion of the homogeneous model with respect to the saturated model when the distribution of the variables is not simply a Poisson distribution.
— Be able to perform these likelihood calculations within the framework of uncertainty models from multiple sources, thus taking into account both variability due to measurement (stochastic aspect of measurement) and variability due to the compositional variability of the material (consequence of material alteration processes — taphonomy);
— Study the effectiveness of the likelihood loss criterion in the context of other segmentation algorithms (we have already demonstrated the effectiveness of this criterion in a k-means type algorithm), but also for factorisation algorithms (as an extension of positive matrix factorisation algorithms).

In concrete terms, the thesis work will provide both a theoretical contribution to the above-mentioned issues and an implementation component (numerical calculation, efficient implementation and applications).

Contexte de travail

The PhD will be supervised by the IPANEMA laboratory (CNRS/MNHN/Ministry of Culture/University of Versailles Saint-Quentin, Gif-sur-Yvette; https://ipanema.cnrs.fr/) and co-supervised by the SOLEIL synchrotron. The affiliated doctoral school will be the Hadamard Mathematics Doctoral School (EDMH) at Paris-Saclay University.
The successful candidate will be based mainly at IPANEMA on the SOLEIL synchrotron site. IPANEMA is a joint laboratory of the CNRS, the Ministry of Culture, the University of Versailles Saint-Quentin-en-Yvelines and the National Museum of Natural History (UAR 3461). The laboratory conducts methodological research aimed at the advanced characterisation of materials from archaeology, palaeoenvironments, palaeontology and cultural heritage, and supports synchrotron research by hosting external users. The PhD student will be based mainly at IPANEMA and will work regularly at the SOLEIL premises. Regular meetings involving both entities will be held.

Additional information

The candidate must enjoy working both independently and in a highly interdisciplinary and collaborative environment. Good communication skills and a written and spoken understanding of English are required for disseminating results to the international scientific community in the relevant fields.

Contraintes et risques

None