  This paper addresses the challenge of reconstructing a 3D power spectrum map
from sparse, scattered, and incomplete spectrum measurements. It proposes an
integrated approach combining interpolation and block-term tensor decomposition
(BTD). This approach leverages an interpolation model with the BTD structure to
exploit the spatial correlation of power spectrum maps. Additionally, nuclear
norm regularization is incorporated to effectively capture the low-rank
characteristics. To implement this approach, a novel algorithm that combines
alternating regression with singular value thresholding is developed.
Analytical justification for the enhancement provided by the BTD structure in
interpolating power spectrum maps is provided, yielding several important
theoretical insights. The analysis explores the impact of the spectrum on the
error in the proposed method and compares it to conventional local polynomial
interpolation. Extensive numerical results demonstrate that the proposed method
outperforms state-of-the-art methods in terms of signal source separation and
power spectrum map construction, and remains stable under off-grid measurements
and inhomogeneous measurement topologies.
