  Detection of a signal under noise is a classical signal processing problem.
When monitoring spatial phenomena under a fixed budget, i.e., either physical,
economical or computational constraints, the selection of a subset of available
sensors, referred to as sparse sensing, that meets both the budget and
performance requirements is highly desirable. Unfortunately, the subset
selection problem for detection under dependent observations is combinatorial
in nature and suboptimal subset selection algorithms must be employed. In this
work, different from the widely used convex relaxation of the problem, we
leverage submodularity, the diminishing returns property, to provide practical
near optimal algorithms suitable for large-scale subset selection. This is
achieved by means of low-complexity greedy algorithms, which incur a reduced
computational complexity compared to their convex counterparts.
