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Alternating steepest descent methods for tensor completion with applications to spectromicroscopy
Oliver Townsend, Sergey Dolgov, Silvia Gazzola, Misha Kilmer
https://arxiv.org/abs/2506.10661

Alternating steepest descent methods for tensor completion with applications to spectromicroscopy
In this paper we develop two new Tensor Alternating Steepest Descent algorithms for tensor completion in the low-rank $\star_{M}$-product format, whereby we aim to reconstruct an entire low-rank tensor from a small number of measurements thereof. Both algorithms are rooted in the Alternating Steepest Descent (ASD) method for matrix completion, first proposed in [J. Tanner and K. Wei, Appl. Comput. Harmon. Anal., 40 (2016), pp. 417-429]. In deriving the new methods we target the X-ray spectromic…