  Matrix $\mathbf{C}$ can be blindly deconvoluted if there exist matrices
$\mathbf{A}$ and $\mathbf{B}$ such that $\mathbf{C}= \mathbf{A} \ast
\mathbf{B}$, where $\ast$ denotes the operation of matrix convolution. We study
the problem of matrix deconvolution in the case where matrix $\mathbf{C}$ is
proportional to the inverse of the autocovariance matrix of an autoregressive
process. We show that the deconvolution of such matrices is important in
problems of Hankel structured low-rank approximation (HSLRA). In the cases of
autoregressive models of orders one and two, we fully characterize the range of
parameters where such deconvolution can be performed and provide construction
schemes for performing deconvolutions. We also consider general autoregressive
models of order $p$, where we prove that the deconvolution $\mathbf{C}=
\mathbf{A} \ast \mathbf{B}$ does not exist if the matrix $\mathbf{B}$ is
diagonal and its size is larger than $p$.
