  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.
