Tensor Matched Kronecker-Structured Subspace Detection for Missing Information

We consider the problem of detecting whether a tensor signal having many missing entities lies within a given low dimensional Kronecker-Structured (KS) subspace. This is a matched subspace detection problem. Tensor matched subspace detection problem is more challenging because of the intertwined signal dimensions. We solve this problem by projecting the signal onto the Kronecker structured subspace, which is a Kronecker product of different subspaces corresponding to each signal dimension. Under this framework, we define the KS subspaces and the orthogonal projection of the signal onto the KS subspace. We prove that reliable detection is possible as long as the cardinality of the missing signal is greater than the dimensions of the KS subspace by bounding the residual energy of the sampling signal with high probability.