  This paper explores an energy-modified leverage sampling strategy for matrix
completion in radio map construction. The main goal is to address potential
identifiability issues in matrix completion with sparse observations by using a
probabilistic sampling approach. Although conventional leverage sampling is
commonly employed for designing sampling patterns, it often assigns high
sampling probability to locations with low received signal strength (RSS)
values, leading to a low sampling efficiency. Theoretical analysis demonstrates
that the leverage score produces pseudo images of sources, and in the regions
around the source locations, the leverage probability is asymptotically
consistent with the RSS. Based on this finding, an energy-modified leverage
probability-based sampling strategy is investigated for efficient sampling.
Numerical demonstrations indicate that the proposed sampling strategy can
decrease the normalized mean squared error (NMSE) of radio map construction by
more than 10% for both matrix completion and interpolation-assisted matrix
completion schemes, compared to conventional methods.
