  The detection and localization of a target from samples of its generated
field is a problem of interest in a broad range of applications. Often, the
target field admits structural properties that enable the design of lower
sample detection strategies with good performance. This paper designs a
sampling and localization strategy which exploits separability and unimodality
in target fields and theoretically analyzes the trade-off achieved between
sampling density, noise level and convergence rate of localization. In
particular, the strategy adopts an exploration-exploitation approach to target
detection and utilizes the theory of low-rank matrix completion, coupled with
unimodal regression, on decaying and approximately separable target fields. The
assumptions on the field are fairly generic and are applicable to many decay
profiles since no specific knowledge of the field is necessary, besides its
admittance of an approximately rank-one representation. Extensive numerical
experiments and comparisons are performed to test the efficacy and robustness
of the presented approach. Numerical results suggest that the proposed strategy
outperforms algorithms based on mean-shift clustering, surface interpolation
and naive low-rank matrix completion with peak detection, under low sampling
density.
