International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 03 Issue: 01 | Jan-2016 www.irjet.net p-ISSN: 2395-0072 © 2016, IRJET | Impact Factor value: 4.45 | ISO 9001:2008 Certified Journal | Page 613 Efficient Data Gathering with Compressive Sensing in Wireless Sensor Networks Nikhil S. Hage 1 , Mrs.S.Kayalvizhi 2 1 M-Tech (Embedded system technology), Former IEEE member, SRM UNIVERSITY, CHENNAI-603203,INDIA, Email:nikhil0724@gmail.com 2 Assistant professor, Department of Electronics and Communication Engineering, SRM UNIVERSITY, CHENNAI-603203,INDIA ---------------------------------------------------------------------***--------------------------------------------------------------------- Abstract -In this paper, we study the problem of data gathering with compressive sensing (CS) in wireless sensor networks (WSNs). Unlike the conventional approaches, which require uniform sampling in the traditional CS theory, the wireless sensor networks are very useful in such area where the human being is unable to go and monitor. In such areas the continuous monitoring is require without failure of network or nodes but wireless sensors network have some energy constrain and cost constrain. we propose a random walk algorithm for data gathering in WSNs and for future purpose we can compare the result of random walk approach to chain based algorithm for data gathering which is traditional algorithm regularly used for network formation in WSNs. Random walk algorithm approach will absorb the constrain like path constrain for network efficiently and give non-uniform measurement. In this paper, from the perspectives of Compressive sensing theory and graph theory, we provide mathematical foundations to allow random measurements to be collected in a random walk based manner We obtain random matrix from expander graph which will constructed by node measurement and for reconstructing we use l1 minimization theorem. Comparing two approaches with respect to their probability of data gathering .we also carry out simulation of both the scheme. Simulation result shows that our proposed scheme random walk approach can significantly reduce communication cost and reduce noise. Key Words: Random walk, Compressive sensing, l1- minimization, Gaussian and binomial function, Data gathering. 1. INTRODUCTION As we know, in the past few years, wireless sensor networks (WSNs) have been deployed in a wide range of application scenarios, such as battle field surveillance, environment monitoring, and security systems. We consider data collection problem in large-scale WSNs. sensor are deployed to monitor physical phenomena such as temperature, humidity and light over geometric area. Data gathering is one of most important functions provided by WSNs, where sensor will sense the data collect all data and transfer this data to one another i.e. from nodes to sink or sink to nodes. Due to the fact that there may exist high correlations among these sensor readings, it is inefficient to directly deliver raw data to the destination. Many techniques that attempt to reduce the traffic load have been developed, such as distributed compression algorithms [2], [3] and distributed source coding (DSC) approaches [3], [4]. However, the classical compression techniques for WSNs, [1], [2], [4], [5], [9], [18]. Typically associated with routing algorithms, impose high computation and communication overhead on sensor nodes. We have various kind of technique to study and apply to networks i.e. WSNs networks to collect data Compressive data gathering using sub-Gaussian random matrix which use term as opportunistic pipelining to data gather [8].forming chain-based networks To data gathering explain in chain- based protocol under compressive sensing framework[9]. In that paper the some protocol for energy efficient data gathering are explain such as LEACH[9] which is cluster- based method to collect data and another one is PEGASIS[9](Power-Efficient Gathering In Sensor Information System) which is chain-based method to collect data in networks. Various other papers will discuss about application on data gathering with or without compressive sensing method. In particular the compressive sensing method is now most emerging technique in the field of wireless network which will give more advantages than any other sampling theorem spatially Shannon sampling theorem or Nyquist theorem .as we know conventional approaches to sampling signals or image follow shannonǯs theorem: the sampling rate must be at least the twice the maximum frequency present in the signal so called Nyquist rate. Main fact is that, this principle will only consider nearly all the signal acquisition protocol used in consumer audio and video electronics, medical imaging devices, radio receivers, and so on. For some signal such as images that are not naturally