  We consider the problem of joint estimation of structured inverse covariance
matrices. We perform the estimation using groups of measurements with different
covariances of the same unknown structure. Assuming the inverse covariances to
span a low dimensional linear subspace in the space of symmetric matrices, our
aim is to determine this structure. It is then utilized to improve the
estimation of the inverse covariances. We propose a novel optimization
algorithm discovering and exploiting the underlying structure and provide its
efficient implementation. Numerical simulations are presented to illustrate the
performance benefits of the proposed algorithm.
