Subject Training

The tensor Block-Block Terms Decomposition (BBTD) has been recently introduced in the literature [1] as a novel decomposition of a fourth-order tensor into an outer product of two low-rank matrices. The BBTD provides a generalization of the well-known block term decomposition (BTD) and is a powerful tool for matrix-valued imaging applications. While initial progress has been made in recent works, further theoretical studies are needed on aspects such as uniqueness and estimation algorithms, as well as the connections of the BBTD to new signal processing applications.

The topic of the proposed internship takes a deeper dive into this new tensor decomposition by exploring new forms of BBTD. On the one hand, we shall generalize it to higher orders and derive the associated estimation algorithms. Such a generalization, on the other hand, will open new possibilities of applications, especially in wireless communication systems, including the modeling of advanced multi-antenna transceiver schemes, near-field array signal processing, and joint channel estimation and equalization.

[1] BARRETO, Saulo Cardoso, FLAMANT, Julien, MIRON, Sebastian, et al. Tensor Block-Block Terms Decomposition for Matrix-Valued Imaging Applications. 2025 (https://hal.science/hal-05059862v1)