Statistical Performance of Convex Low-Rank and Sparse Tensor Recovery

Abstract

Suppose a tensor * ∈ ℝn1x...xnK is low-Tucker-rank and sparse simultaneously. The statistical performance of recovering * from it from its noisy observations is studied mathematically in this paper. A convex optimization problem like Remurs [1] which integrates l1-norm and the tensor nuclear norm is proposed. Theoretically, the deterministic upper bound of the estimation error is provided for general noise based on the assumption of restricted strong convexity. For the tensor de-noising problem and the tensor compressive sensing problem, non-asymptotic upper bounds of the estimation error are also shown when the noise is i.i.d. Gaussian.