\title{A Method for Joint Compressing and Recovering Destructed Signals in Wireless Multimedia Sensor Networks}

\author{M. Eslami, F. Torkamani-Azar, E. Mehrshahi \\
Faculty of Electrical and Computer Engineering \\
ShahidBeheshti University, G. C., Tehran}

\begin{abstract}
The WSNs are developed to sense, gather, process and transmit the real-world information and so in recent years, solving numerous challenges of wireless sensor networking are considered intensely. In addition, in Wireless Multimedia Sensor Networks intra- and inter-signal correlations can be exploited in the theory of distributed source coding and similarly in distributed compressive sensing to compress signals as much as possible. These cases may be occurred in applications and services in which work with smart spaces and context aware networks.In this paper based on compressive sensing a framework denoted asECMis proposed to compress and reconstruct the signals of the sensors even for networks which the data transmission is imperfect.ECM uses the concepts of distributed compressive sensing and the shared information between sensor's signals to compress the signals more.
\end{abstract}

\textbf{Keywords –} Wireless Sensor Network, Distributed Compressive Sensing, Signal Compression,

\section{INTRODUCTION}

The Wireless sensor networks (WSN) provide a flexible way to monitor the physical parameters of the environment through the deployment of a large number of sensor nodes. There are three main challenges in WSN, i.e., network lifetime, computational ability and bandwidth constraints. With the availability of low-energy and low-cost multimedia devices, such as microphones and cameras, which may capture multimedia contents from the field, the next generation WSNs, Wireless Multimedia Sensor Networks (WMSN) have been proposed and drawn the immediate attention of the research community \cite{1}.

Suppose there are Jsensors in the region, measuring a phenomenon in spatio-temporal manner. A Fusion Center (FC) gets all the measurements and runs an algorithm which jointly decodes the signals of the sensors and reconstructs the phenomenon at the sensor positions. In cases that there is a significant correlation between sensors' signals, the joint decoding based on Distributed Source Coding (DSC) \cite{2} could be used in the FC to decompress the transmitted sensors' signals. Using DSC methods can increase compression rate so that data can be transmitted by consuming less power and bandwidth.

On the other hand, Compressive Sensing (CS) is a sampling theory \cite{3}, which leverages the compressibility of the signal to reduce the number of samples required for reconstruction and significantly reduces costs of sampling and computation at a sensor with restricted capabilities. CS theory exhibits that a signal with a sparse transform representation can be reconstructed from a small set of irrelevant random projections. CS technique as the data acquisition approach in a WSN can significantly reduce the energy consumed in the process of sampling and transmission through the network, and also lower the wireless bandwidth required for communication.

CS can also be applied in distributed scenario similar to distributed source coding (DSC). The theory of Distributed Compressive Sensing (DCS) \cite{4} uses inter- and intra- signal correlations, for proposing new distributed source coding and compression algorithms for multi-signal ensembles based on CS theory. In a typical DCS setting and Joint Sparsity Model (JSM) \cite{4}, each sensor compresses its signal individually by means of projecting it on an incoherent basis and transmits the compressed information (actually sensed) to the Fusion Center (FC). If the right conditions exist, FC can reconstruct jointly all the signals considering that the measured signal of each sensor is individually sparse in some basis.

Current paper proposes method for compressing the signals of a WMSN and reducing the amount of the transmitted data. In the regarded WMSN, the captured signal of each sensor should be transmitted to a central unit (or FC) through a wireless interface. In addition signals of the sensors