# Hyperspectral Imagery Super-Resolution by Adaptive POCS and Blur Metric

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## Abstract

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## 1. Introduction

## 2. Projection onto Convex Set-Based Super-Resolution Reconstruction (SRR)

## 3. Hyperspectral Imagery Super-Resolution by Adaptive Projection onto Convex Sets (APOCS) and Blur Metric

#### 3.1. Image Blur Metric Based on Gabor Wavelet Transform

Algorithm 1. Steps of the image blur metric assessment method: |

Step 1: Set the initial value of p (Equation (5)); |

Step 2: Compute the Gabor feature GF(m_{1},m_{2}) via Equation (4); |

Step 3: Compute the mean value m(m_{1},m_{2}) and variance value ε(m_{1},m_{2}) of the Gabor feature with Equations (5) and (6); |

Step 4: Compute the adaptive threshold t(m_{1},m_{2}) (Equation (7)) and achieve the Gabor feature classification (Equation (8)); |

Step 5: Gain the separated frequency information HFR(m_{1},m_{2}) and LFR(m_{1},m_{2}) via Equation (9); |

Step 6: Extract the statistical features HFR_{had}(m_{1},m_{2}), HFR_{mhad}, HFR_{vad}(m_{1},m_{2}), HFR_{mvad} and LFR_{had}(m_{1},m_{2}), LFR_{mhad}, LFR_{vad}(m_{1},m_{2}), LFR_{mvad} from the separated frequency information (Equations (10) and (11)); |

Step 7: Compute the image blur metric assessment A_{IBM} via statistical features (Equation (12)). |

#### 3.2. Proposed APOCS-Blur Metrics (BM) Method

Algorithm 2. Steps of the proposed APOCS-BM method: |

Step 1: Set the initial value of p (Equation (5)), α, β, t_{0} (Equation (13)) and iteration number Itn; |

Step 2: Gain the initial HR image H from the LR image L_{1} by linear interpolation, calculate the A_{IBM}[m_{1},m_{2}] and ${A}_{IBM}^{LR}$ for each LR image L_{1}~L_{4}; |

Step 3: For i = 1,2, …, Itn |

for j = 1,2, 3, 4 |

Step 3.1: Calculate the affine motion parameters for LR image L_{j}; |

Step 3.2: Gain the estimation value H_{es} of H via the affine motion parameters and point spread function; |

Step 3.3: Calculate the residual R_{j}(i); |

Step 3.4: Calculate the adaptive threshold value δ_{k}[m_{1},m_{2}]; |

Step 3.5: If R_{j}(i) > δ_{k}[m_{1},m_{2}] or R_{j}(i) < −δ_{k}[m_{1},m_{2}] |

Step 3.5.1: refresh H with the estimation value H_{es}; |

end If |

end for |

end for |

Step 4: output the reconstructed HR image H. |

## 4. Experiments and Results

#### 4.1. PaviaU and PaviaC Dataset

#### 4.2. Jinyin Tan Dataset

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Blur images gained from the Pavia university dataset with a 5 × 5 Gaussian kernel of different standard deviations. (

**a**) The standard deviation of Gaussian kernel is 0.1; (

**b**) the standard deviation of Gaussian kernel is 0.5; (

**c**) the standard deviation of Gaussian kernel is 1; (

**d**) the standard deviation of Gaussian kernel is 2. (

**a**) ${A}_{IBM}=1.3588$; (

**b**) ${A}_{IBM}=1.3366$; (

**c**) ${A}_{IBM}=1.2952$; (

**d**) ${A}_{IBM}=1.2473$.

**Figure 4.**False color image of experimental results for the PaviaU dataset (color composite of R: 80, G: 28, B: 9). (

**a**) original HR image; (

**b**) linear interpolation results; (

**c**) DCT-based method [10] results; (

**d**) Kim [19] results; (

**e**) POCS [17] results; (

**f**) SRSR [20] results; (

**g**) proposed APOCS-BM method results.

**Figure 5.**Spectral curves of pixel (181, 23) in the PaviaU dataset. (

**a**) Spectral curves of different methods; (

**b**) Difference values of spectral curves (the black dotted line is the baseline, the red line represents the results of the proposed methods); (

**c**) spectral curve location.

**Figure 6.**False color image of experimental results for the PaviaC dataset (color composite of R: 80, G: 28, B: 9). (

**a**) original HR image; (

**b**) linear interpolation results; (

**c**) DCT-based method [10] results; (

**d**) Kim [19] results; (

**e**) POCS [17] results; (

**f**) SRSR [20] results; (

**g**) proposed APOCS-BM method results.

**Figure 7.**Spectral curves of pixel (233,163) in the PaviaC dataset. (

**a**) Spectral curves of different methods; (

**b**) Difference values of spectral curves (the black dotted line is the baseline, the red line illustrates the results of the proposed methods); (

**c**) spectral curve location.

**Figure 8.**False color image of Jinyin Tan dataset 1 (water box) and Jinyin Tan dataset 2 (grassland) captured from the Jinyin Tan dataset, color composite of R: 48, G: 30, B: 11.

**Figure 9.**False color image of experimental results for the Jinyin Tan dataset 1 (color composite of R: 48, G: 30, B: 11). (

**a**) original HR image; (

**b**) linear interpolation results; (

**c**) DCT-based method [10] results; (

**d**) Kim [19] results; (

**e**) POCS [17] results; (

**f**) SRSR [20] results; (

**g**) proposed APOCS-BM method results.

**Figure 10.**Spectral curves of pixel (82, 184) in the Jinyin Tan dataset 1. (

**a**) Spectral curves of different methods; (

**b**) Difference values of spectral curves (the black dotted line is the baseline, the red line represents the results of the proposed methods); (

**c**) spectral curve location.

**Figure 11.**False color image of experimental results for the Jinyin Tan dataset 2 (color composite of R: 48, G: 30, B: 11). (

**a**) original HR image; (

**b**) linear interpolation results; (

**c**) DCT-based method [10] results; (

**d**) Kim [19] results; (

**e**) POCS [17] results; (

**f**) SRSR [20] results; (

**g**) proposed APOCS-BM method results.

**Figure 12.**Spectral curves of pixel (182, 44) in the Jinyin Tan dataset 2. (

**a**) Spectral curves of different methods; (

**b**) Difference values of spectral curves (the black dotted line is the baseline, the red line shows the results of the proposed methods); (

**c**) spectral curve location.

Measures | Linear Interpolation | DCT-Based Method [10] | Kim [19] | POCS [17] | SR-SR Method [20] | Proposed Method |
---|---|---|---|---|---|---|

A-PSNR | 20.8478 | 24.9727 | 25.1193 | 25.7390 | 26.9570 | 28.5050 |

A-SSIM | 0.5347 | 0.6824 | 0.7108 | 0.7161 | 0.8069 | 0.8435 |

SAM | 0.2148 | 0.1192 | 0.1100 | 0.1002 | 0.1016 | 0.0817 |

Measures | Linear Interpolation | DCT-Based Method [10] | Kim [19] | POCS [17] | SR-SR Method [20] | Proposed Method |
---|---|---|---|---|---|---|

A-PSNR | 21.4309 | 25.6022 | 25.7052 | 26.3187 | 27.3867 | 29.0013 |

A-SSIM | 0.4959 | 0.6539 | 0.6761 | 0.6816 | 0.7916 | 0.8292 |

SAM | 0.2633 | 0.1333 | 0.1225 | 0.1093 | 0.1208 | 0.0949 |

Measures | Linear Interpolation | DCT-Based Method [10] | Kim [19] | POCS [17] | SR-SR Method [20] | Proposed Method |
---|---|---|---|---|---|---|

A-PSNR | 37.9661 | 40.0457 | 40.0424 | 40.1739 | 43.8014 | 44.7879 |

A-SSIM | 0.9608 | 0.9696 | 0.9720 | 0.9727 | 0.9869 | 0.9885 |

SAM | 0.0876 | 0.0621 | 0.0600 | 0.0572 | 0.0588 | 0.0411 |

Measures | Line Interpolation | DCT-Based Method [10] | Kim [19] | POCS [17] | SR-SR Method [20] | Proposed Method |
---|---|---|---|---|---|---|

A-PSNR | 47.3629 | 52.4696 | 50.7218 | 50.7808 | 51.1665 | 55.5370 |

A-SSIM | 0.9897 | 0.9905 | 0.9910 | 0.9914 | 0.9947 | 0.9966 |

SAM | 0.0610 | 0.0544 | 0.0474 | 0.0488 | 0.0448 | 0.0405 |

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**MDPI and ACS Style**

Hu, S.; Zhang, S.; Zhang, A.; Chai, S.
Hyperspectral Imagery Super-Resolution by Adaptive POCS and Blur Metric. *Sensors* **2017**, *17*, 82.
https://doi.org/10.3390/s17010082

**AMA Style**

Hu S, Zhang S, Zhang A, Chai S.
Hyperspectral Imagery Super-Resolution by Adaptive POCS and Blur Metric. *Sensors*. 2017; 17(1):82.
https://doi.org/10.3390/s17010082

**Chicago/Turabian Style**

Hu, Shaoxing, Shuyu Zhang, Aiwu Zhang, and Shatuo Chai.
2017. "Hyperspectral Imagery Super-Resolution by Adaptive POCS and Blur Metric" *Sensors* 17, no. 1: 82.
https://doi.org/10.3390/s17010082