Compressive Sensing (CS) shows high promise for fully distributed
compression in wireless sensor networks (WSNs). In theory, CS
allows the approximation of the readings from a sensor field with
excellent accuracy, while collecting only a small fra
ction of them at
a data gathering point. However, the conditions under which CS
performs well are not necessarily met in practice. CS requires a
suitable transformation that makes the signal sparse in its domain.
Also, the transformation of the data given by the routing protocol
and network topology and the sparse representation of the signal
have to be incoherent, which is not straightforward to achieve in
real networks. In this paper we investigated the effectiveness of
data recovery through joint Compressive Sensing (CS) and
Principal Component Analysis (PCA) in actual WSN deployments.
We proposed a novel system, called CS-PCA that embeds a
feedback control mechanism to automatically change the
compression ratio through changing the number of transmitting
sensors, while bounding the reconstruction error. The considered
recovery techniques in the proposed system are: biharmonic Spline
(Spline), Deterministic Ordinary Least Square (DOLS),
Probabilistic Ordinary Least Square (POLS) and Joint CS and PCA
(CS-PCA). We found that the later outperform all other
interpolation technique in the case of slow varying signals, while
POLS was the most effective in case of fast varying signals that(
low correlation less than 0.45)
