On the benefit of using tight frames for robust data transmission and compressive data gathering in wireless sensor networks

Compressive sensing (CS), a new sampling paradigm, has recently found several applications in wireless sensor networks (WSNs). In this paper, we investigate the design of novel sensing matrices which lead to good expected-case performance - a typical performance indicator in practice - rather than the conventional worst-case performance that is usually employed when assessing CS applications. In particular, we show that tight frames perform much better than the common CS Gaussian matrices in terms of the reconstruction average mean squared error (MSE). We also showcase the benefits of tight frames in two WSN applications, which involve: i) robustness to data sample losses; and ii) reduction of the communication cost.