Generic order-4 symmetric tensors of rank up to 2n+1 are efficiently decomposable via moment matrix extension, with a conjectured extension to O(n^2) rank.
Spectral decomposition of a 4th-order covariance tensor: Applications to diffusion tensor MRI
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Efficient Tensor Decomposition via Moment Matrix Extension
Generic order-4 symmetric tensors of rank up to 2n+1 are efficiently decomposable via moment matrix extension, with a conjectured extension to O(n^2) rank.