1 research outputs found
Provable Near-Optimal Low-Multilinear-Rank Tensor Recovery
We consider the problem of recovering a low-multilinear-rank tensor from a
small amount of linear measurements. We show that the Riemannian gradient
algorithm initialized by one step of iterative hard thresholding can
reconstruct an order- tensor of size and multilinear
rank with high probability from only
measurements, assuming is a constant. This sampling complexity is optimal
in , compared to existing results whose sampling complexities are all
unnecessarily large in . The analysis relies on the tensor restricted
isometry property (TRIP) and the geometry of the manifold of all tensors with a
fixed multilinear rank. High computational efficiency of our algorithm is also
achieved by doing higher order singular value decomposition on intermediate
small tensors of size only rather than on tensors of
size as usual