Compressive sensing for wireless sensor networks

Abstract

This chapter introduces the fundamental concepts that are important in the study of compressive sensing (CS). We present the mathematical model of CS where the use of sparse signal representation is emphasized. We describe three conditions, i.e., the null space property (NSP), the restricted isometry property (RIP) and mutual coherence, that are used to evaluate the quality of sensing matrices and to demonstrate the feasibility of reconstruction. We briefly review some widely used numerical algorithms for sparse recovery, which are classified into two categories, i.e., convex optimization algorithms and greedy algorithms. Finally, we illustrate various examples where the CS principle has been applied to deal with various problems occurring in wireless sensor networks.