  Envisioned as the next-generation transceiver technology, the holographic
multiple-input-multiple-output (HMIMO) garners attention for its superior
capabilities of fabricating electromagnetic (EM) waves. However, the densely
packed antenna elements significantly increase the dimension of the HMIMO
channel matrix, rendering traditional channel estimation methods inefficient.
While the dimension curse can be relieved to avoid the proportional increase
with the antenna density using the state-of-the-art wavenumber-domain sparse
representation, the sparse recovery complexity remains tied to the order of
non-zero elements in the sparse channel, which still considerably exceeds the
number of scatterers. By modeling the inherent clustered sparsity using a
Gaussian mixed model (GMM)-based von Mises-Fisher (vMF) distribution, the
to-be-estimated channel characteristics can be compressed to the scatterer
level. Upon the sparsity extraction, a novel wavenumber-domain
expectation-maximization (WD-EM) algorithm is proposed to implement the
cluster-by-cluster variational inference, thus significantly reducing the
computational complexity. Simulation results verify the robustness of the
proposed scheme across overheads and signal-to-noise ratio (SNR).
