  In this survey paper, our goal is to discuss recent advances of compressive
sensing (CS) based solutions in wireless sensor networks (WSNs) including the
main ongoing/recent research efforts, challenges and research trends in this
area. In WSNs, CS based techniques are well motivated by not only the sparsity
prior observed in different forms but also by the requirement of efficient
in-network processing in terms of transmit power and communication bandwidth
even with nonsparse signals. In order to apply CS in a variety of WSN
applications efficiently, there are several factors to be considered beyond the
standard CS framework. We start the discussion with a brief introduction to the
theory of CS and then describe the motivational factors behind the potential
use of CS in WSN applications. Then, we identify three main areas along which
the standard CS framework is extended so that CS can be efficiently applied to
solve a variety of problems specific to WSNs. In particular, we emphasize on
the significance of extending the CS framework to (i). take communication
constraints into account while designing projection matrices and reconstruction
algorithms for signal reconstruction in centralized as well in decentralized
settings, (ii) solve a variety of inference problems such as detection,
classification and parameter estimation, with compressed data without signal
reconstruction and (iii) take practical communication aspects such as
measurement quantization, physical layer secrecy constraints, and imperfect
channel conditions into account. Finally, open research issues and challenges
are discussed in order to provide perspectives for future research directions.
