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CS^{2}-Collector: A New Approach for Data Collection in Wireless Sensor Networks Based on Two-Dimensional Compressive Sensing

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## Abstract

**:**

^{2}-collector, for WSNs based on the theory of Two Dimensional Compressive Sensing (2DCS). It exploits both temporal and spatial sparsity, i.e., 2D-sparsity of WSNs and achieves significant gain on the tradeoff between the compression ratio and reconstruction accuracy as the numerical simulations and evaluations on different types of sensors’ data. More intuitively, with the same given energy budget, CS

^{2}-collector provides significantly more accurate reconstruction of the profile of the physical phenomena that are temporal-spatially sparse.

## 1. Introduction

^{2}-collector, for WSNs based on the theory of two-dimensional CS (2DCS) by exploiting the two-Dimensional sparsity (2D-sparsity), i.e., the temporal and spatial sparsity, existing in most of WSNs. Like our evaluations on different types of real world sensors’ data, CS

^{2}-collector produces significant performance gain on signal reconstruction accuracy compared with the traditional one-dimensional CS (1DCS) based approaches with the same compression ratio or energy consumption budget. In other words, with the same goal of reconstruction accuracy, CS

^{2}-collector requires a significantly less amount of data transmitted through the network to the base station so that the energy consumption can be reduced.

^{2}-collector in detail. The numerical simulations and real world dataset evaluations are presented in Section 5. In Section 6, we conclude the whole paper.

## 2. Related Work

## 3. Introduction to Compressive Sensing

## 4. CS${}^{2}$-Collector for Data Collection in WSNs

#### 4.1. System Architecture

#### 4.2. CS${}^{2}$-Collector

**1**s, this operation is equal to randomly selecting ${m}_{s}$ sensors to submit their compressed data vector to base stations. It is known that, in the theory of CS, most of the information can be preserved by randomly choosing a small subset of the sensors. It has been proved in [8] that this sparse projection matrix satisfies the RIP condition. Because only a small subset of sensors are required to submit their data, the overall energy consumption during data transmission is reduced significantly.

#### 4.3. Data Matrix Reconstruction at Base Station

#### 4.3.1. Two-Dimensional Sparsity

#### 4.3.2. Kronecker Product for ${\ell}_{1}$ Optimisation

## 5. Performance Evaluation

#### 5.1. Goals, Metrics and Methodologies

#### 5.2. Numerical Simulations

#### 5.3. Performance Evaluations on Real Dataset

#### 5.3.1. Intel Berkley Lab WSN Dataset

#### 5.3.2. Dataset Preprocessing

#### 5.3.3. Temperature Data

#### 5.3.4. Humidity Data and Voltage Data

#### 5.3.5. Lighting Data

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 2.**Performance of 2DCS and 1DCS on random sparse matrix with value of non-zero elements is 1.

Device | Duty Cycle | Average Current | The Ratio of Energy |
---|---|---|---|

Sensors | 1.67% | 9 ($\mathsf{\mu}$A) | 3.8% |

Radio | 1% | 206 ($\mathsf{\mu}$A) | 86% |

Microcontroller | 0.4% | 9.6 ($\mathsf{\mu}$A) | 4% |

Quiescent | - | 15 ($\mathsf{\mu}$A) | 6.2% |

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**MDPI and ACS Style**

Wang, Y.; Yang, Z.; Zhang, J.; Li, F.; Wen, H.; Shen, Y. CS^{2}-Collector: A New Approach for Data Collection in Wireless Sensor Networks Based on Two-Dimensional Compressive Sensing. *Sensors* **2016**, *16*, 1318.
https://doi.org/10.3390/s16081318

**AMA Style**

Wang Y, Yang Z, Zhang J, Li F, Wen H, Shen Y. CS^{2}-Collector: A New Approach for Data Collection in Wireless Sensor Networks Based on Two-Dimensional Compressive Sensing. *Sensors*. 2016; 16(8):1318.
https://doi.org/10.3390/s16081318

**Chicago/Turabian Style**

Wang, Yong, Zhuoshi Yang, Jianpei Zhang, Feng Li, Hongkai Wen, and Yiran Shen. 2016. "CS^{2}-Collector: A New Approach for Data Collection in Wireless Sensor Networks Based on Two-Dimensional Compressive Sensing" *Sensors* 16, no. 8: 1318.
https://doi.org/10.3390/s16081318