Ph. D. Project
Physics-informed methods for learning low-rank models in polarization imaging. Application to cancer cell detection in bio-imaging.
2022/09/28 - 2025/09/27
Context: Polarization information plays a major role in imaging. It allows to capture important characteristics of the observed medium, such as shape,
roughness, orientation, physicochemical prop- erties, etc. [1], [2]. These different features, often inaccessible to conventional intensity measurements, are
crucial descriptors in many applications, including bioimaging characterization of cancerous tissues / cells [3].

Goals: Despite the numerous applications of polarization imaging, exploiting its full potential requires the development of new methodological tools that
take into account the different physical constraints specific to the measurement and interpretation of polarization. This Ph.D. project aims at addressing these
issues by focusing on the development of physics-informed methods to learn low- rank models from datasets of polarized images. The expected
contributions will span theoretical (e.g. uniqueness conditions) and methodological (e.g. efficient algorithms) aspects. A complementary objective of this
thesis will be to demonstrate, in collaboration with biology researchers at CRAN, the relevance of polarization to detect cancer cells in biological

Research program: The Ph.D. candidate will focus on developping new low rank-models for both passive and active polarization imaging. As a first step,
he/she will focus on dimension reduction techniques for Stokes parameter datasets - a set of four energetic parameters widely used to describe polarization
properties in passive imaging. Given the large amount of Stokes data which can be collected in a growing range of applications thanks to the rapid
emergence of polarization cameras, di- mension reduction techniques are essential to ensure that physically relevant features can be rigorously inferred from
data. This is a key step before further processing (clustering, classification, regression, etc. ) To this aim the Ph.D. candidate will take advantage of recent
low-rank matrix factorization tools introduced in [5], which exploit geometric / algebraic representations of Stokes parameter data using quaternions. He/she
will study identifiability properties and propose novel algorithms to efficiently solve the factorization problem.

As a second task, he/she will investigate the problem of low-rank modelling for matrix-valued polarization images. This modality, known as Mueller matrix
imaging [6] permits the complete char- acterization of the polarization properties of a given medium, and is thus widely used in biomedical imaging [7]. As
a promising new approach, such datasets will be represented as higher-order tensors for which the Ph.D. candidate will develop relevant low-rank tensor
decomposition models and algorithms [8]. Just like above, a crucial aspect of this work will focus on preserving the physical relevance of the reduced model
while enabling the addition of prior information and maintaining tractable algorithms.

The various theoretical and methodological contributions expected from this work will be validated around original applications in bio-imaging. This work,
carried out in collaboration with the project "Molecular targets in a translational approach" of the BioSiS department of CRAN, will aim to demonstrate the
potential of polarimetric information in bio-imaging. Two imaging modalities will be considered: high-resolution polarimetric camera imaging and
polarimetric spectro-microscopy. The confrontation with experimental results will feed the development of methodological tools and inversely.

[1] J. S. Tyo, D. L. Goldstein, D. B. Chenault, et al., "Review of passive imaging polarimetry for remote sensing applications," Applied optics, vol. 45, no.
22, pp. 5453-5469, 2006.
[2] N. Ghosh and A. I. Vitkin, "Tissue polarimetry: Concepts, challenges, applications, and outlook," Journal of biomedical optics, vol. 16, no. 11, p. 110
801, 2011.
[3] A. Pierangelo, A. Benali, M.-R. Antonelli, et al., "Ex-vivo characterization of human colon cancer by mueller polarimetric imaging," Optics express,
vol. 19, no. 2, pp. 1582-1593, 2011.
[4] S.-M. Guo, L.-H. Yeh, J. Folkesson, et al., "Revealing architectural order with quantitative label-free imaging and deep learning," en, eLife, vol. 9,
e55502, Jul. 2020, issn: 2050-084X. doi: 10.7554/eLife. 55502. [Online]. Available: (visited on 11/24/2020).
[5] J. Flamant, S. Miron, and D. Brie, "Quaternion non-negative matrix factorization: Definition, uniqueness, and algorithm," IEEE Transactions on Signal
Processing, vol. 68, pp. 1870-1883, 2020.
[6] J. Gil and R. Ossikovski, Polarized Light and the Mueller matrix approach. CRC Press, 2016, isbn: 9781482251562.
[7] C. He, H. He, J. Chang, et al., "Characterizing microstructures of cancerous tissues using multispectral transformed mueller matrix polarization
parameters," Biomedical optics express, vol. 6, no. 8, pp. 2934- 2945, 2015.
[8] N. D. Sidiropoulos, L. De Lathauwer, X. Fu, et al., "Tensor decomposition for signal processing and machine learning," IEEE Transactions on Signal
Processing, vol. 65, no. 13, pp. 3551-3582, 2017.
Biology, Signals and Systems in Cancer and Neuroscience