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.

Key points:

• Design smaller (per mode) subfilters instead of the full one-dimensional filter 
• Computational complexity reduction for large-scale filtering problems
• Better convergence properties than linear filtering

Figure 10: Multilinear filtering concept based on tensor decomposition.

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

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[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.