1. Compressive Sensing Based on Local Regional Data in Wireless Sensor Networks Hao Yang, Liusheng Huang, Hongli Xu, Wei Yang 2012 IEEE Wireless Communications and Networking Conference: Mobile and Wireless Networks

2. Outline Introduction Compressive Sensing Theory Compressive Sensing for Local Region – Spatial-Temporal Correlation – Random Distribution – Gaussian Distribution Experiments Conclusion

3. Introduction (1/3) Reducing energy consumption of sensors is an especial important problem to prolong the lifetime of wireless sensor networks. Compressive Sensing (CS), as a novel and effective signal transform technology, has been proposed in different fields, such as medical and image [1,2]. [1] J. Haldar, and D. Hernando, and ZP Liang, “Compressed Sensing in MRI with non-Fourier encoding”, IEEE Trans. Med. Imag, vol. 30, pp. 893–903, 2011. [2] J. Wu, and F. Liu, and LC Jiao, and X.Wang, “Compressive Sensing SAR Image Reconstruction Based on Bayesian Framework and Evolutionary Computation”, IEEE Trans. Image Processing, no. 99, pp. 1-1, 2011.

4. Compressive sensing is a data acquisition technique that aims to measure sparse and compressible signals which can be recovered exactly from very few measurements. Nyquist rate – a lower bound for the sample rate for alias-free signal sampling Compressive Sampling/Sensing – a novel sensing/sampling against the common wisdom in data acquisition Introduction (2/3)

5. It is difficult to promote the advantage of the technology in actual applications in WSNs due to the characteristic of itself. The effect of using CS technique depends immensely on whether the feature (sparsity) of the signal is known beforehand. In this paper, a CS approach based on local regional data is presented and verified in actual environments. Introduction (3/3)

6. Compressive Sensing Theory (1/4) Compressive sensing (also known as compressed sensing, compressive sampling, or sparse sampling) Compressive sensing is the reconstruction of sparse signals from very few samples.

7. Compressive Sensing Theory (2/4)

8. Compressive Sensing Theory (3/4)

9. Compressive Sensing Theory (4/4)

10. Distributed Compressive Sensing (DCS) Distributed Compressed Sensing (DCS) is proposed to exploit both intra- and inter-signal correlation structures. In a typical DCS scenario, a number of sensors measure signals (of any dimension) that are each individually sparse in some basis and also correlated from sensor to sensor. This theory rests on a concept, which is called Joint Sparsity Model (JSM). [9] M.F. Duarte, and S. Sarvotham, and D. Baron, and M.B. Wakin, and R.G. Baraniuk, “Distributed Compressed Sensing of Jointly Sparse Signals”, Asilomar Conf. Signals, Sys., Comput, pp. 1537-1541, 2005.

11. Joint Sparsity Model (JSM)

12. common componentindividual component

13. Compressive Sensing for Local Region (1/2) Sensors usually gather data from their surroundings and they may be similar with each other if they are closed in geographically. In the other words, both time and space are not independent in actual environments. Owning to synchronized tendency of changing among the relative sensors, it is possible that relative sizes of data gathered by sensors in a local region would not alter frequently.

14. Spatial-Temporal Correlation – Information Relation (IR) – Alternation Relation (AR) – Spatial-Temporal Correlation Model (STCM) Compressive Methods – Random Distribution – Gaussian Distribution Compressive Sensing for Local Region (2/2)

15. Information Relation (IR)

16. Alternation Relation (AR)

17. Spatial-Temporal Correlation Model (STCM)

18. Random Distribution (1/5)

19. Random Distribution (2/5)

20. Random Distribution (3/5)

21. In the second step for compressing, an increasing rate which called relation_rate is proposed in order to abstract more common value based on the above conclusion. Random Distribution (4/5)

22. Based on the above process of compressing, the elements of the signal F are probably close to zero. When the usage of CS, matrix cm_1 and cm_2 could be multiplied by original measurement matrix to get a new measurement matrix. Random Distribution (5/5)

23. In generally, there exists a kind of the data whose distributions usually obey the Gaussian distribution in real applications. Gaussian Distribution (1/2)

24. According to the probability density function of the standard normal distribution, the common component s(i) can be estimated as below. In formula (13), norminv() denotes the inverse function of the accumulation function of the probability and i/N is the accumulation probability. It is worthwhile that the accumulation probability should be multiplied a modified coefficient in case of its value reaches 1. In the usage of CS, the process in this situation is the same as the above description. Gaussian Distribution (2/2)

25. Experiments In actual experiments, sensors are placed both indoors and outdoors. Temperature and illumination in the local regions are observed. In the usage of CS technique in the paper, Discrete Cosine Transform (DCT), Fast Fourier transform (FFT) and Discrete Wavelet Transform (DWT) will be used as sparse transform matrixes [10-12].

26. Experiments - Actual Environment The number of IRIS sensors in this experiments is 32, which gather temperature and illumination 3 times in every minute. For comparing to effects in simulation environments, data are transformed every 2, 5, 10, 20 minutes and reconstructed together as one signal based on l1 -algorithm by the sink sensor after receiving data eight times and the number of samples M is 15. That is, N=32*8=256.

27. Experiments - Simulation Environments Random distribution.

28. Experiments - Simulation Environments Gaussian distribution

29. Analysis of Efficiency

30. Conclusion In this paper, a compressive sensing algorithm is present based on spatial-temporal correlation for actual applications in WSNs. The paper analyzes the feature of data in local regions and proposes a reasonable model, STCM, to emerge the relationship among data of sensors. Two algorithms targeted to two kinds of data distributions are designed to optimize measurement matrix of CS. Experiments in actual environments and simulation environment shows our algorithms outperforms other traditional methods. Just once extra transmission for every sensor.