  In this paper, we investigate the sparse channel estimation in holographic
multiple-input multiple-output (HMIMO) systems. The conventional angular-domain
representation fails to capture the continuous angular power spectrum
characterized by the spatially-stationary electromagnetic random field, thus
leading to the ambiguous detection of the significant angular power, which is
referred to as the power leakage. To tackle this challenge, the HMIMO channel
is represented in the wavenumber domain for exploring its cluster-dominated
sparsity. Specifically, a finite set of Fourier harmonics acts as a series of
sampling probes to encapsulate the integral of the power spectrum over specific
angular regions. This technique effectively eliminates power leakage resulting
from power mismatches induced by the use of discrete angular-domain probes.
Next, the channel estimation problem is recast as a sparse recovery of the
significant angular power spectrum over the continuous integration region. We
then propose an accompanying graph-cut-based swap expansion (GCSE) algorithm to
extract beneficial sparsity inherent in HMIMO channels. Numerical results
demonstrate that this wavenumber-domainbased GCSE approach achieves robust
performance with rapid convergence.
