# Adaptive Compressive Sensing and Data Recovery for Periodical Monitoring Wireless Sensor Networks

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## Abstract

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## 1. Introduction

- We propose an adaptive compressive sensing framework for periodical monitoring of WSNs, where a reconstruction error estimation module is designed to check whether the current sampling rate is still sufficient for signal reconstruction, and a sparsity determination module is designed to estimate the sparsity and calculate the required sampling rate at the next monitoring period.
- We propose an efficient sparsity variation determination algorithm, which can determine the current sparsity as well as the new sampling rate by only re-sampling a few measurements to save the energy cost and guarantee the recovery performance.
- We propose an improved SAMP algorithm to recover the signal with unknown sparsity, where both the linear and non-linear step size variation are designed to guarantee fast convergence and reliable accuracy.
- We evaluate the proposed algorithms with extensive simulations and study the impacts of multiple environmental factors, including the number of sensors and the different sampling rates. The simulation results show that our proposed algorithm could achieve substantial improvements compared with existing algorithms in terms of sparsity matching and signal recovery.

## 2. Data Gathering Based on Compressive Sensing

Algorithm 1: Compressive sampling with sampling rate M |

## 3. Adaptive Sampling for Signals with Dynamic Sparsity

**Lemma**

**1.**

Algorithm 2: Adaptive compressive sampling |

## 4. Signal Recovery with Unknown Sparsity

Algorithm 3: Adaptive compressive sampling |

## 5. Numerical Results

#### 5.1. Sparsity Analysis

#### 5.2. Adaptive Sampling

#### 5.3. Signal Recovery

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 5.**(

**a**) Raw signal from monitoring the sea temperature, (

**b**) sparse analysis of the raw signal in the Discrete Wavelet Transform (DWT) domain.

**Figure 6.**(

**a**) Raw RSSI signal of a smartphone from a real environment, (

**b**) sparse analysis of the raw signal based on the K-SVD algorithm.

Algorithm | ROMP | SAMP-1 | SAMP-3 | RAMP | LA-SAMP | nLA-SAMP |
---|---|---|---|---|---|---|

Time(s) | 0.344 | 1.622 | 0.542 | 0.453 | 0.437 | 0.438 |

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**MDPI and ACS Style**

Chen, J.; Jia, J.; Deng, Y.; Wang, X.; Aghvami, A.-H. Adaptive Compressive Sensing and Data Recovery for Periodical Monitoring Wireless Sensor Networks. *Sensors* **2018**, *18*, 3369.
https://doi.org/10.3390/s18103369

**AMA Style**

Chen J, Jia J, Deng Y, Wang X, Aghvami A-H. Adaptive Compressive Sensing and Data Recovery for Periodical Monitoring Wireless Sensor Networks. *Sensors*. 2018; 18(10):3369.
https://doi.org/10.3390/s18103369

**Chicago/Turabian Style**

Chen, Jian, Jie Jia, Yansha Deng, Xingwei Wang, and Abdol-Hamid Aghvami. 2018. "Adaptive Compressive Sensing and Data Recovery for Periodical Monitoring Wireless Sensor Networks" *Sensors* 18, no. 10: 3369.
https://doi.org/10.3390/s18103369