Low-rank and sparse tensor decompositions with applications in signal processing
| Quand ? |
Le 16/01/2025, de 01:00 à 02:00 |
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| Participants |
Cesar CAIAFA |
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Cesar CAIAFA, Senior research scientist at IAR-CONICET and University of Buenos Aires, Argentina
Title: “Low-rank and sparse tensor decompositions with applications in signal processing”
Abstract: In this talk, I will present low-rank and sparse versions of the Tucker tensor decomposition model, highlighting their applications in signal processing. I will begin with an introduction to tensors and multilinear algebra, followed by a discussion of the Tucker decomposition and its role in achieving efficient data compression and representation. I will demonstrate how tensors can be reconstructed from subsampled data by assuming a low multilinear rank structure. Then, to address the curse of dimensionality in sparse coding for multidimensional data, I will introduce the Sparse Tucker model. Both the low-rank and sparse Tucker models enable the generalization of classical Compressed Sensing (CS) theory from one-dimensional to multidimensional signals. I will illustrate these concepts with examples of linear inverse problems, including tensor completion and the reconstruction of Magnetic Resonance Images (MRI) from compressive multiway projections. Finally, I will present the ENCODE model, a Sparse Tucker decomposition designed to model diffusion MRI measurements, which facilitates brain connectomics studies by achieving substantial data compression and reducing computational costs.