Abstract / truncated to 115 words (read the full abstract)

Today’s society is characterized by an abundance of data that is generated at an unprecedented velocity. However, much of this data is immediately thrown away by compression or information extraction. In a compressed sensing (CS) setting the inherent sparsity in many datasets is exploited by avoiding the acquisition of superfluous data in the first place. We combine this technique with tensors, or multiway arrays of numerical values, which are higher-order generalizations of vectors and matrices. As the number of entries scales exponentially in the order, tensor problems are often large-scale. We show that the combination of simple, low-rank tensor decompositions with CS effectively alleviates or even breaks the so-called curse of dimensionality. After discussing the ... toggle 21 keywords

tensor – canonical polyadic decomposition – large-scale – signal processing – blind source separation – multilinear algebra – numerical algorithms – optimization – big data – randomization – tucker decomposition – multilinear singular value decomposition – tensorlab – software – multilinear systems – implicit tensors – updating – tracking – compressed sensing – tensor completion – structured tensors

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