Trainee Project
Learning physical features from polarimetric images with constrained matrix factorizations
2022/03/01 - 2022/08/31
Polarization information plays a major role in imaging. It allows to capture important characteristics of the observed medium, such as shape, roughness,
orientation, physicochemical properties, etc. [1, 2] These different features, often inaccessible to conventional intensity measurements, are key descriptors in
many applications, including bioimaging characterization of cancerous tissues [3]


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 M2R internship will focus on developing
efficient algorithms to learn meaningful low-rank features from datasets of polarized images. As a first task, the candidate will study 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, dimension
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 candidate will take advantage of recent low-rank matrix factorization tools introduced in [4], which exploit geometric / algebraic
representations of Stokes parameter data using quaternions. He/she will propose novel algorithms to efficiently solve this constrained factorization problem.
The proposed algorithms will be extensively benchmarked on both synthetic and experimental datasets from spectropolarimetry and polarization
microscopy -- both important applications modalities available at CRAN.

[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] 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.
Biology, Signals and Systems in Cancer and Neuroscience