Low rank tensor recovery via iterative hard thresholding

• Published in: Linear algebra and its applications Vol. 523; pp. 220 - 262
• Main Authors: Rauhut, Holger, Schneider, Reinhold, Stojanac, Željka
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 15.06.2017; American Elsevier Company, Inc
• Subjects: Gaussian random ensemble; Hierarchical tensor format; Higher order singular value decomposition; Iterative hard thresholding; Linear algebra; Low rank recovery; Random partial Fourier ensemble; Tensor completion; Tensor decompositions; Tensor train decomposition; Higher order singular value decomposition; Iterative hard thresholding; Random partial Fourier ensemble; Hierarchical tensor format; 15A69; Low rank recovery; Tensor train decomposition; 15B52; Tensor completion; Gaussian random ensemble; 65Fxx; Tensor decompositions; 94A20

We study extensions of compressive sensing and low rank matrix recovery (matrix completion) to the recovery of low rank tensors of higher order from a small number of linear measurements. While the theoretical understanding of low rank matrix recovery is already well-developed, only few contribution...