Tensor Decompositions for Multilinear Filtering

Multilinear filtering conceptFigure 10: Multilinear filtering concept based on tensor decomposition.

When high-dimensional systems are modeled and optimized, linear methods often perform unsatisfactorily due to their slow convergence and the high number of parameters to estimate, which brings high computational and storage complexities. To cope with these difficulties, computationally efficient low-rank tensor filtering offers attractive solutions. The approach can overcome the curse of dimensionality, improving performance in large-scale systems.

Key points of multilinear filtering include designing smaller subfilters (per mode) instead of using full one-dimensional filters, which helps to reduce computational complexity in large-scale filtering problems. Moreover, the method offers better convergence properties compared to traditional linear filtering techniques.

References

[1] M. Dehghan, J. Henrique de M. Goulart, A. L. F. de Almeida, “Low-rank multilinear filtering,” Digital Signal Processing, 2024.

[2] B. Sokal, P. R. B. Gomes, A. L. F. de Almeida, B. Makki, G. Fodor, “Reducing the control overhead of intelligent reconfigurable surfaces via a tensor-based low-rank factorization approach,” IEEE Transactions on Wireless Communications, vol. 22, no. 10, pp. 6578-6593, 2023.

[3] L. N. Ribeiro, A. L. F. de Almeida, J. A. Nossek, J. C. M. Mota, “Low-complexity separable beamformers for massive antenna array systems,” IET Signal Processing, vol. 13, pp. 434-442, 2019.

[4] L. N. Ribeiro, A. L. F. de Almeida, J. C. M. Mota, “Tensor beamforming for multilinear translation invariant arrays,” IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Shanghai, 2016.