Canonical Polyadic (CP) Decomposition of Structured Semi-Symmetric Fourth-Order Tensors

摘要

This paper considers canonical polyadic decomposition of fourth order tensors which have both structured and unstructured factors. The structured factors are assumed to be sub-selected rows of Vandermonde matrices. We show that for a M × N × M × N tensor with M (resp. N) being the dimension corresponding to structured (resp. unstructured) factors, recovery of O(M²N) factors are possible, if the structured factors are designed according to specific non-uniform sampling geometries. Our proposed algorithm is only based on simple linear algebraic operations, and can easily be implemented.