  This paper investigates the channel estimation for holographic MIMO systems
by unmasking their distinctions from the conventional one. Specifically, we
elucidate that the channel estimation, subject to holographic MIMO's
electromagnetically large antenna arrays, has to discriminate not only the
angles of a user/scatterer but also its distance information, namely the
three-dimensional (3D) azimuth and elevation angles plus the distance (AED)
parameters. As the angular-domain representation fails to characterize the
sparsity inherent in holographic MIMO channels, the tightly coupled 3D AED
parameters are firstly decomposed for independently constructing their own
covariance matrices. Then, the recovery of each individual parameter can be
structured as a compressive sensing (CS) problem by harnessing the covariance
matrix constructed. This pair of techniques contribute to a parametric
decomposition and compressed deconstruction (DeRe) framework, along with a
formulation of the maximum likelihood estimation for each parameter. Then, an
efficient algorithm, namely DeRe-based variational Bayesian inference and
message passing (DeRe-VM), is proposed for the sharp detection of the 3D AED
parameters and the robust recovery of sparse channels. Finally, the proposed
channel estimation regime is confirmed to be of great robustness in
accommodating different channel conditions, regardless of the near-field and
far-field contexts of a holographic MIMO system, as well as an improved
performance in comparison to the state-of-the-art benchmarks.
