  Our interest lies in the recoverability properties of compressed tensors
under the \textit{canonical polyadic decomposition} (CPD) model. The considered
problem is well-motivated in many applications, e.g., hyperspectral image and
video compression. Prior work studied this problem under somewhat special
assumptions---e.g., the latent factors of the tensor are sparse or drawn from
absolutely continuous distributions. We offer an alternative result: We show
that if the tensor is compressed by a subgaussian linear mapping, then the
tensor is recoverable if the number of measurements is on the same order of
magnitude as that of the model parameters---without strong assumptions on the
latent factors. Our proof is based on deriving a \textit{restricted isometry
property} (R.I.P.) under the CPD model via set covering techniques, and thus
exhibits a flavor of classic compressive sensing. The new recoverability result
enriches the understanding to the compressed CP tensor recovery problem; it
offers theoretical guarantees for recovering tensors whose elements are not
necessarily continuous or sparse.
