In this paper, we propose a novel compressive

sensing (CS) based approach for sparse target counting and

positioning in wireless sensor networks. While this is not the

first work on applying CS to count and localize targets, it

is the first to rigorously justify the validity of the problem

formulation. Moreover, we propose a novel greedy matching

pursuit algorithm (GMP) that complements the well-known

signal recovery algorithms in CS theory and prove that GMP can

accurately recover a sparse signal with a high probability. We

also propose a framework for counting and positioning targets

from multiple categories, a novel problem that has never been

addressed before. Finally, we perform a comprehensive set of

simulations whose results demonstrate the superiority of our

approach over the existing CS and non-CS based techniques.