PhD Student (f/m) for X-ray fluorescence tomography in the Algo. and Sci. Data Analylisis group

The European Synchrotron, the ESRF, is an international research centre based in Grenoble, France.

Through its innovative engineering, pioneering scientific vision and a strong commitment from its 700 staff members, the ESRF is recognised as one of the top research facilities worldwide. Its particle accelerator produces intense X-ray beams that are used by thousands of scientists each year for experiments in diverse fields such as biology, medicine, environmental sciences, cultural heritage, materials science, and physics.

Supported by 21 countries, the ESRF is an equal opportunity employer and encourages diversity. 

Thesis subject: Hybrid physics- and data-driven methods for X-ray fluorescence computed tomography (XRFCT) Scientific context and motivation X-ray fluorescence CT (XRFCT) is based on the analysis of the fluorescence signal of a sample excited by a thin X-ray pencil beam. It has several applications in the fields of material science, earth and environmental science and biomedicine. For example, it is used to track specific elements in biological tissues (e.g.prostate) orin combination with heavynano-particles which serve as a fluorescence probe. In earth sciences, XRFCT has been used to determine elemental composition of meteorites fragments.

In XRFCT, the sample is excited with a monochromatic pencil beam (see Figure 1). Interactions of the imping- ing beam with the sample's atoms produce fluorescence photons, whose energy is characteristic of the chemical element. A fluorescence detector collects all fluorescence photons with high energy resolution, for many sample positions and orientations. The collected spectra are then fitted to elemental data and finally passed on to a tomographic reconstruction algorithm to produce 3D spatial elemental maps. 

Unlike absorption tomography, the attenuation along the impinging and the emitted X-rays must be accounted for in the reconstruction algorithm. Early theoretical works introduced analytic and possibly exact inversion formulas, assuming a complete sampling of the projection space (i.e. full angular coverage, non-truncated projections). In many cases though, these conditions cannot be met and iterative methods like MLEM or SART become solutions of choice.

Among the technical challenges that prevent XRFCT to becoming a routine 3D technique, one can cite:

- Non complete angular coverage of the acquisition: due to mechanical / technical constraints, angular coverage of the sample cannot exceed 120 degrees approximately.

- Alignment: During the several-hour-long acquisition, the sample may drift. The image quality depends crucially on the accurate identification of these drifts. 

- Sample radiation damage: due to the very small size of the sample, the radiation dose may induce sample deformation, which makes the whole dataset inconsistent. 

Scientific goals and technical approach

Derive practical consistency conditions for XRFCT.

Data Consistency conditions (DCC) are mathematical relations that are satisfied by a set of data if it is consistent with their physics model. In some cases, self-absorption of the fluorescence signal can be neglected, and Helgason-Ludwig[1], conditions can be efficient. But in other cases, self-absorption is too significant and must be accounted for. No DCC exist for the fluorescence forward model. Finding such DCC may allow to better guide the estimation of the alignment parameters. The project will benefit from the long-time expertise in the field of DCC developed by the supervisors[2].

[1] Ludwig D., Comm. on Pure and Applied Mathematics, 1966.

[2] Lesaint et al., IEEE TRPMS, 2017.

Design hybrid data/physics driven alignment methods.

To further push the accuracy of the critical alignment procedure, we plan to explore methods that combine the universal expressivity of deep neural networks with physics-informed techniques (e.g. DCC-based techniques). Recent research has proved that convolutional networks can be efficient in geometric calibration of transmission CT data[3]. More recently, gradient-based geometric calibration methods combined with deep-learning techniques have investigated these hybrid-methods for classical CT[4].

[3]Xiao and Yan, Applied Optics, 2021.

[4]Schoonhoven et al., Optics Express, 2024.

Generalize hybrid methods to the XRFCT reconstruction problem.

Finally, the hybrid methods will be extended to the full 3D XRFCT reconstruction problem. It has been shown that learned inverse problem methods are all the more effective as the data are very noisy. The severe acquisition conditions (under-sampling, missing wedge, low signal) found in XRFCT make these methods good candidates: we can expect from these methods a significant improvement of the image quality compared to state-of-the-art regularization-based variational methods. 

For more information, please contact Jérome Lesaint (jerome.lesaint@esrf.fr) or Simon Rit (simon.rit@creatis.insa-lyon.fr).

- Master degree (or equivalent diploma that entitles the candidate to enroll for a PhD) in applied maths or computer sciences. Master in Physics with strong interest in applied maths/computer sciences is also possible.

- Proficiency in signal and image processing.

- Knowledge of X-ray physics would be a plus.

- Autonomy, creativity, ability to work within an interdisciplinary team (physics, computer sciences, mathematics, instrumentation).

- Programming language: Python mainly (C++/CUDA optionally).

- Excellent written and oral English (working language at ESRF).

The salary will be calculated on the basis of relevant qualifications and professional experience.

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- Join an innovative international research institute, with a workforce from 38 different countries

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- Benefit from our competitive compensation and allowances package, including financial support for your relocation to Grenoble For further information on employment terms and conditions, please refer to https://www.esrf.fr/home/Jobs/what-we-offer.html

The ESRF is an equal opportunity employer and encourages applications from disabled persons.