Mathematics in signal processing V

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Differential-geometric Newton method for the best rank-(R1, R2, R3) approximation of tensors (2008, background): “In the literature, decompositions are considered where the tensor corresponding to S is as diagonal as possible (in a least squares sense) [8, 16, 36], or where the original tensor is decomposed in a minimal number of rank-1 terms (CANDECOMP/PARAFAC) [7, 9, 10, 17, 27], on which orthogonal constrain”
On the third secant variety (2011, background): “siderable amount of recent research on ranks and border ranks of tensors, see, e.g., [15, 9] and references therein. In signal processing one is interested in determining ranks of tensors, see, e.g., [6] and references therein. In computational complexity, one looks for exotic algorithms via limits ”
Riemannian Optimization on Tensor Products of Grassmann Manifolds: Applications to Generalized Rayleigh-Quotients (2010, background): “Classical application areas of such low-rank approximations can be found in statistics, signal processing and data compression [4, 20, 21, 31].”