Abstract— Due to the large availability of raw data, the appeal for data fusion has been steadily growing in the signal processing community. Hence the design of coupled models, that exploit shared information between several observations. It is thus expected from data fusion that it provides a better estimation of the parameters of interest rather than separate processing of the datasets.
In remote sensing, hyperspectral images have been thoroughly exploited in, e.g., spectral unmixing, image classification or target detection. The natural 3-dimensional format of these images allows them to be mathematically represented as 3-dimensional tensors.
In this presentation, I will introduce some of my recent results regarding multimodal data fusion using low-rank tensor decompositions, applied on hyperspectral images. I will focus on the hyperspectral super-resolution and spectral unmixing problems accounting for inter-image variability. While the first one addresses image reconstruction, the second one falls under the scope of source separation. A major difficulty lies in the presence of inter-image variability, that reinforces the ill-posedness of the problems. I will introduce two algorithms to solve the problems at hand. Then, I will showcase their performance for image fusion and spectral unmixing on a set of real hyperspectral data accounting for spectral variability.
If time permits, I will illustrate the statistical performance of the proposed approach, using a new randomly-constrained Cramér-Rao bound.
Biography— Clémence Prévost is currently a post-doctoral fellow in CRIStAL, University of Lille, under the supervision of Pierre Chainais and Rémy Boyer. She received the PhD degree in signal processing in 2021 from CRAN, University of Nancy. Her main research interests include multimodal data fusion, tensor decompositions and solving ill-posed inverse problems.
References— Prévost, C., Borsoi, R. A., Usevich, K., Brie, D., Bermudez, J. C., & Richard, C. (2022). Hyperspectral super-resolution accounting for spectral variability: coupled tensor LL1-based recovery and blind unmixing of the unknown super-resolution image. SIAM Journal on Imaging Sciences, 15(1), 110-138.
