Journal
INVERSE PROBLEMS
Volume 27, Issue 2, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0266-5611/27/2/025010
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Funding
- Japan Society for the Promotion of Science (JSPS) [DC2]
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In this paper we consider sparsity on a tensor level, as given by the n-rank of a tensor. In an important sparse-vector approximation problem (compressed sensing) and the low-rank matrix recovery problem, using a convex relaxation technique proved to be a valuable solution strategy. Here, we will adapt these techniques to the tensor setting. We use the n-rank of a tensor as a sparsity measure and consider the low-n-rank tensor recovery problem, i.e. the problem of finding the tensor of the lowest n-rank that fulfills some linear constraints. We introduce a tractable convex relaxation of the n-rank and propose efficient algorithms to solve the low-n-rank tensor recovery problem numerically. The algorithms are based on the Douglas-Rachford splitting technique and its dual variant, the alternating direction method of multipliers.
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