# Adaptive Grouping Distributed Compressive Sensing Reconstruction of Plant Hyperspectral Data

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Spectral Adaptive Distributed Compressive Sensing

#### 2.2. Analysis of Plant Spectral Characteristics

#### 2.3. Joint Sparse Model

_{i}and X

_{i+}

_{1}, the correlation between X

_{i}and X

_{i+}

_{1}can be calculated, where X

_{i}represents the current band. As the result of different wavelength reflection of the same object in the different bands of hyperspectral images, X

_{i}and X

_{i+}

_{1}have the same spatial information. Meanwhile, X

_{i}and X

_{i+}

_{1}have their own unique spectral information. The X

_{i}and X

_{i+}

_{1}can be described as follows:

_{i}= X

_{c}+ X

_{i_r}

_{i+1}= X

_{c}+ X

_{i+1_r}

_{c}is the same part of X

_{i}and X

_{i+}

_{1}, which refers to the same spatial information, X

_{i_r}and X

_{i+}

_{1_r}are their own unique parts, which mean the results of different reflections of different wavelengths. X

_{i}is used as a reference to X

_{i+}

_{1}, and the same spectral estimation (X

_{c}) and the different information error coding (X

_{i+}

_{1_r}) are used as the predictive value of X

_{i+}

_{1}in the spectral coding. The joint sparse model can be expressed as below:

_{i}= ΨS

_{i}

_{i+1_r}= ΨS

_{i+1_r}

_{i}and S

_{i+}

_{1_r}are sparse representations of X

_{i}and X

_{i+}

_{1_r}, respectively, and Ψ is a canonical orthogonal matrix.

#### 2.4. Distributed Compressive Sensing Based on Spectral Characteristics

_{i}= ΦX

_{i}= ΦΨS

_{i}

_{i}is a sparse representation of the original signal in the transform domain, Ψ

^{H}Ψ = ΨΨ

^{H}= I, and I is a unit matrix. The size of the Φ is M × N, M << N, which is the partial block Hadamard matrix [28]. X

_{i}is a band of hyperspectral data, and Y

_{i}is an observed value.

_{0}norm is an NP-hard problem. The minimization problem of l

_{1}norm is equivalent to that of l

_{0}norm under certain conditions [29], so Equation (6) can be transformed to Equation (7). In this paper, GPSR and OMP are chosen to reconstruct X

_{i}on the basis of the Y

_{i}:

#### 2.5. Spectral Adaptive Grouping and Selection of Key Bands

- Step 1: Solve all PSNRs between the first band and each of the rest of the bands, and those in the rest of the bands and those whose PSNRs are greater than the threshold are all selected and classified into the group of the first band.
- Step 2: Set up a new set from the remaining bands and repeat Step 1 to construct a new group.
- Step 3: Repeat Step 2 until all bands are assigned to different groups.

#### 2.6. Error Evaluation Methods

## 3. Results and Discussion

#### 3.1. The Results of Spectral Adaptive Threshold Grouping

#### 3.1.1. The Results of Adaptive Grouping and the Different Sampling Rate of Key and Non-Key Bands

#### 3.1.2. Analysis of Results of Adaptive Band Grouping Reconstruction

#### 3.2. Spatial Domain Reconstruction Analysis

#### 3.3. Spectral Domain Reconstruction Results Analysis

#### 3.4. Results of Spectral Indices of Physiological Properties

#### 3.5. Results of Average Reconstructed Time

#### 3.6. Discussion

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Spatial image of hyperspectral raw data and three regional spectral curves. (

**a**) Original data space image; (

**b**) The averaged spectrum for each ROI.

**Figure 8.**Comparison of reconstruction results for different algorithms at different sampling rates.

Threshold/dB | Groups | Sampling Rate/bpp | ||||
---|---|---|---|---|---|---|

0.1 | 0.2 | 0.3 | 0.4 | 0.5 | ||

20 | 6 | 0.092 | 0.194 | 0.296 | 0.398 | 0.500 |

21 | 7 | 0.091 | 0.193 | 0.296 | 0.398 | 0.500 |

22 | 7 | 0.091 | 0.193 | 0.296 | 0.398 | 0.500 |

23 | 8 | 0.090 | 0.192 | 0.295 | 0.397 | 0.500 |

24 | 15 | 0.080 | 0.185 | 0.290 | 0.395 | 0.500 |

25 | 21 | 0.072 | 0.179 | 0.286 | 0.393 | 0.500 |

26 | 29 | 0.060 | 0.170 | 0.280 | 0.390 | 0.500 |

27 | 36 | 0.049 | 0.162 | 0.275 | 0.387 | 0.500 |

28 | 45 | 0.035 | 0.151 | 0.267 | 0.384 | 0.500 |

29 | 56 | 0.015 | 0.136 | 0.258 | 0.379 | 0.500 |

Error Analysis of Different Algorithms | Sampling Rate/bpp | |||||
---|---|---|---|---|---|---|

0.1 | 0.2 | 0.3 | 0.4 | 0.5 | ||

MAPE | OMP | 0.9683 | 0.5158 | 0.2861 | 0.2105 | 0.1598 |

GPSR | 0.1560 | 0.1006 | 0.0796 | 0.0689 | 0.0617 | |

AGDCS | 0.1005 | 0.0814 | 0.0728 | 0.0680 | 0.0639 | |

MAE | OMP | 0.4599 | 0.2408 | 0.1434 | 0.1035 | 0.0787 |

GPSR | 0.0798 | 0.0529 | 0.0424 | 0.0369 | 0.0329 | |

AGDCS | 0.0544 | 0.0451 | 0.0401 | 0.0370 | 0.0345 | |

RMSE | OMP | 0.5722 | 0.3003 | 0.1803 | 0.1303 | 0.0994 |

GPSR | 0.1065 | 0.0698 | 0.0556 | 0.0481 | 0.0428 | |

AGDCS | 0.0710 | 0.0580 | 0.0519 | 0.0479 | 0.0447 |

Index Analysis of Different Algorithms | Sampling Rate/bpp | |||||
---|---|---|---|---|---|---|

0.1 | 0.2 | 0.3 | 0.4 | 0.5 | ||

ROI1 | OMP | 15.196 | 1.216 | 24.319 | 10.768 | 1.027 |

GPSR | 0.499 | 0.209 | 0.219 | 0.187 | 0.267 | |

AGDCS | 0.262 | 0.623 | 0.514 | 0.495 | 0.377 | |

ROI2 | OMP | 1.683 | 7.504 | 0.773 | 81.952 | 0.778 |

GPSR | 0.628 | 0.481 | 0.372 | 0.359 | 0.292 | |

AGDCS | 0.535 | 0.410 | 0.345 | 0.375 | 0.432 | |

ROI3 | OMP | 0.623 | 1.116 | 1.400 | 0.707 | 0.538 |

GPSR | 0.536 | 0.225 | 0.206 | 0.209 | 0.200 | |

AGDCS | 0.259 | 0.225 | 0.221 | 0.209 | 0.232 |

Index Analysis of Different Algorithms | Sampling Rate/bpp | |||||
---|---|---|---|---|---|---|

0.1 | 0.2 | 0.3 | 0.4 | 0.5 | ||

ROI1 | OMP | 103.698 | 1.246 | 28.733 | 13.530 | 1.468 |

GPSR | 0.543 | 0.266 | 0.250 | 0.220 | 0.279 | |

AGDCS | 0.2367 | 0.727 | 0.584 | 0.538 | 0.395 | |

ROI2 | OMP | 2.054 | 164.593 | 0.956 | 96.027 | 1.340 |

GPSR | 0.601 | 0.424 | 0.315 | 0.312 | 0.266 | |

AGDCS | 0.513 | 0.405 | 0.333 | 0.350 | 0.403 | |

ROI3 | OMP | 0.691 | 0.950 | 2.181 | 0.728 | 0.557 |

GPSR | 0.667 | 0.314 | 0.245 | 0.270 | 0.273 | |

AGDCS | 0.325 | 0.317 | 0.285 | 0.314 | 0.327 |

Index Analysis of Different Algorithms | Sampling Rate/bpp | |||||
---|---|---|---|---|---|---|

0.1 | 0.2 | 0.3 | 0.4 | 0.5 | ||

ROI1 | OMP | 0.403 | 0.084 | 0.210 | 0.116 | 0.065 |

GPSR | 0.075 | 0.017 | 0.022 | 0.015 | 0.009 | |

AGDCS | 0.032 | 0.008 | 0.006 | 0.011 | 0.009 | |

ROI2 | OMP | 0.092 | 0.291 | 0.085 | 0.095 | 0.043 |

GPSR | 0.080 | 0.049 | 0.037 | 0.032 | 0.025 | |

AGDCS | 0.057 | 0.037 | 0.029 | 0.027 | 0.024 | |

ROI3 | OMP | 0.103 | 0.083 | 0.166 | 0.052 | 0.044 |

GPSR | 0.064 | 0.035 | 0.024 | 0.024 | 0.024 | |

AGDCS | 0.032 | 0.022 | 0.027 | 0.027 | 0.022 |

Index Analysis of Different Algorithms | Sampling Rate/bpp | |||||
---|---|---|---|---|---|---|

0.1 | 0.2 | 0.3 | 0.4 | 0.5 | ||

ROI1 | OMP | 0.362 | 0.061 | 0.106 | 0.078 | 0.059 |

GPSR | 0.093 | 0.013 | 0.022 | 0.019 | 0.018 | |

AGDCS | 0.014 | 0.031 | 0.026 | 0.030 | 0.026 | |

ROI2 | OMP | 0.244 | 0.258 | 0.084 | 0.083 | 0.125 |

GPSR | 0.114 | 0.073 | 0.053 | 0.044 | 0.036 | |

AGDCS | 0.056 | 0.037 | 0.037 | 0.033 | 0.033 | |

ROI3 | OMP | 0.456 | 0.171 | 0.095 | 0.132 | 0.099 |

GPSR | 0.112 | 0.064 | 0.039 | 0.031 | 0.035 | |

AGDCS | 0.051 | 0.036 | 0.033 | 0.027 | 0.028 |

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## Share and Cite

**MDPI and ACS Style**

Xu, P.; Liu, J.; Xue, L.; Zhang, J.; Qiu, B. Adaptive Grouping Distributed Compressive Sensing Reconstruction of Plant Hyperspectral Data. *Sensors* **2017**, *17*, 1322.
https://doi.org/10.3390/s17061322

**AMA Style**

Xu P, Liu J, Xue L, Zhang J, Qiu B. Adaptive Grouping Distributed Compressive Sensing Reconstruction of Plant Hyperspectral Data. *Sensors*. 2017; 17(6):1322.
https://doi.org/10.3390/s17061322

**Chicago/Turabian Style**

Xu, Ping, Junfeng Liu, Lingyun Xue, Jingcheng Zhang, and Bo Qiu. 2017. "Adaptive Grouping Distributed Compressive Sensing Reconstruction of Plant Hyperspectral Data" *Sensors* 17, no. 6: 1322.
https://doi.org/10.3390/s17061322