# A Denoising Method for Randomly Clustered Noise in ICCD Sensing Images Based on Hypergraph Cut and Down Sampling

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Models

#### 2.1. Hypergraph and Hypergraph Cut

#### 2.2. Spectral Clustering

**A**is:

#### 2.3. Robust Principal Component Analysis

## 3. Framework of the Proposed Denoising Algorithm

## 4. The Denoising Algorithm for ICCD Sensing Images

#### 4.1. Over-Segmentation with the Watershed Algorithm

#### 4.2. Down-Sampling and Up-Sampling for Residual Estimation

- (a)
- Calculate the scale of each patch, and then classify them into several classes according to their scale values with the k-means method [27].
- (b)
- For each class, determine the mean of patch scales as the sampling scale in the down-sampling process.
- (c)
- Denoise the image after each down-sampling with the general block-matching and 3D filtering (BM3D) [28] algorithm;
- (d)
- Up-sample each low-resolution image to the original size to obtain a recovered ICCD image.

#### 4.3. Construction of Hyperedges and Their Weights

**A. Construction of a Hyperedge Based on Spectral Clustering**

**B. Calculation of the Hyperedge Weight**

#### 4.4. Patch Classification and Recovery

#### 4.5. Post-Processing by RPCA

## 5. Experiments and Analysis

#### 5.1. Parameter Determination in Constructing the Hypergraph

#### 5.2. Verify the Effectiveness of the Hypergraph Cut

#### 5.3. Verify the Performance of the Proposed Denoising Algorithm

#### 5.4. Verify the Effectiveness of the RPCA in the Denoising Process

#### 5.5. Time Complexity of the Proposed Algorithm

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**An image captured by an ICCD sensor and its noise pattern (enhanced by histogram equalization).

**Figure 4.**Verify the effectiveness of the hypergraph cut. (

**a**) the filtering result based on spectral clustering; (

**b**) the filtering result based on the hypergraph cut.

**Figure 5.**The subjective results of the proposed algorithm and other baselines. (

**a**) the patches in the noisy ICCD image; (

**b**,

**h**,

**n**) the result of the denoising algorithm in [2]; (

**c**,

**i**,

**o**) the result of the proposed algorithm; (

**d**,

**j**,

**p**) the result without the RPCA in Section 4.5; (

**e**,

**k**,

**q**) the results of BM3D; (

**f**,

**l**,

**r**) the result of K-SVD; (

**g**,

**m**,

**s**) the results of BLS-GSM.

**Figure 6.**The subjective results of the proposed algorithm and other baselines. (

**a**) the patches in the noisy ICCD image; (

**b**,

**h**,

**n**) the result of the denoising algorithm in [2]; (

**c**,

**i**,

**o**) the result of the proposed algorithm; (

**d**,

**j**,

**p**) the result without the RPCA in Section 4.5; (

**e**,

**k**,

**q**) the results of BM3D; (

**f**,

**l**,

**r**) the result of K-SVD; (

**g**,

**m**,

**s**) the results of BLS-GSM.

**Figure 7.**The subjective results of the proposed algorithm and other baselines. (

**a**) the patches in the noisy ICCD image; (

**b**,

**h**,

**n**) the result of the denoising algorithm in [2]; (

**c**,

**i**,

**o**) the result of the proposed algorithm; (

**d**,

**j**,

**p**) the result without the RPCA in Section 4.5; (

**e**,

**k**,

**q**) the results of BM3D; (

**f**,

**l**,

**r**) the result of K-SVD; (

**g**,

**m**,

**s**) the results of BLS-GSM.

**Figure 8.**Verify the effectiveness of the RPCA in the filtering process. (

**a**) the results of the RPCA with $\lambda $ = 0.1; (

**b**) the results of the RPCA with $\lambda $ = 0.9; (

**c**) the results of the RPCA with the adaptive parameters.

n | m | $\mathit{\alpha}$ | PSNR (db) | n | m | $\mathit{\alpha}$ | PSNR (db) |
---|---|---|---|---|---|---|---|

2 | 2 | 0.1 | 73.19995 | 3 | 2 | 0.1 | 73.21281 |

2 | 2 | 0.2 | 73.18212 | 3 | 2 | 0.2 | 72.95117 |

2 | 2 | 0.3 | 73.11725 | 3 | 2 | 0.3 | 73.19301 |

2 | 2 | 0.4 | 73.19670 | 3 | 2 | 0.4 | 73.28845 |

2 | 2 | 0.5 | 73.11630 | 3 | 2 | 0.5 | 73.42306 |

2 | 3 | 0.1 | 73.28173 | 3 | 3 | 0.1 | 73.04053 |

2 | 3 | 0.2 | 73.18228 | 3 | 3 | 0.2 | 73.20538 |

2 | 3 | 0.3 | 73.32812 | 3 | 3 | 0.3 | 72.88833 |

2 | 3 | 0.4 | 73.22885 | 3 | 3 | 0.4 | 73.32938 |

2 | 3 | 0.5 | 73.14801 | 3 | 3 | 0.5 | 73.19522 |

2 | 4 | 0.1 | 73.04365 | 3 | 4 | 0.1 | 73.13615 |

2 | 4 | 0.2 | 73.11540 | 3 | 4 | 0.2 | 73.19505 |

2 | 4 | 0.3 | 73.34357 | 3 | 4 | 0.3 | 72.81382 |

2 | 4 | 0.4 | 73.12557 | 3 | 4 | 0.4 | 73.14337 |

2 | 4 | 0.5 | 73.20798 | 3 | 4 | 0.5 | 72.86815 |

2 | 5 | 0.1 | 73.11540 | 3 | 5 | 0.1 | 73.19301 |

2 | 5 | 0.2 | 73.17220 | 3 | 5 | 0.2 | 73.22224 |

2 | 5 | 0.3 | 73.03383 | 3 | 5 | 0.3 | 72.78663 |

2 | 5 | 0.4 | 73.18219 | 3 | 5 | 0.4 | 73.15062 |

2 | 5 | 0.5 | 73.21231 | 3 | 5 | 0.5 | 73.17858 |

4 | 2 | 0.1 | 73.20403 | 5 | 2 | 0.1 | 73.17788 |

4 | 2 | 0.2 | 73.17530 | 5 | 2 | 0.2 | 73.19318 |

4 | 2 | 0.3 | 73.03849 | 5 | 2 | 0.3 | 73.13893 |

4 | 2 | 0.4 | 73.21268 | 5 | 2 | 0.4 | 73.03510 |

4 | 2 | 0.5 | 72.79888 | 5 | 2 | 0.5 | 73.13128 |

4 | 3 | 0.1 | 73.19837 | 5 | 3 | 0.1 | 73.14298 |

4 | 3 | 0.2 | 73.02988 | 5 | 3 | 0.2 | 73.14298 |

4 | 3 | 0.3 | 73.20614 | 5 | 3 | 0.3 | 73.07012 |

4 | 3 | 0.4 | 73.21402 | 5 | 3 | 0.4 | 73.20198 |

4 | 3 | 0.5 | 73.11114 | 5 | 3 | 0.5 | 73.13739 |

4 | 4 | 0.1 | 73.34665 | 5 | 4 | 0.1 | 73.19715 |

4 | 4 | 0.2 | 73.23437 | 5 | 4 | 0.2 | 73.08766 |

4 | 4 | 0.3 | 73.17264 | 5 | 4 | 0.3 | 73.03212 |

4 | 4 | 0.4 | 73.17855 | 5 | 4 | 0.4 | 73.11872 |

4 | 4 | 0.5 | 73.15255 | 5 | 4 | 0.5 | 73.0394 |

4 | 5 | 0.1 | 73.16033 | 5 | 5 | 0.1 | 73.16033 |

4 | 5 | 0.2 | 73.22001 | 5 | 5 | 0.2 | 73.19837 |

4 | 5 | 0.3 | 73.19912 | 5 | 5 | 0.3 | 73.14524 |

4 | 5 | 0.4 | 73.30515 | 5 | 5 | 0.4 | 73.00673 |

4 | 5 | 0.5 | 73.13857 | 5 | 5 | 0.5 | 73.24143 |

Average Runtime | |
---|---|

The algorithm in [2] | 86.3 |

The proposed algorithm without the RPCA | 5.4 |

The proposed algorithm with the RPCA | 57.2 |

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## Share and Cite

**MDPI and ACS Style**

Yang, M.; Wang, F.; Wang, Y.; Zheng, N. A Denoising Method for Randomly Clustered Noise in ICCD Sensing Images Based on Hypergraph Cut and Down Sampling. *Sensors* **2017**, *17*, 2778.
https://doi.org/10.3390/s17122778

**AMA Style**

Yang M, Wang F, Wang Y, Zheng N. A Denoising Method for Randomly Clustered Noise in ICCD Sensing Images Based on Hypergraph Cut and Down Sampling. *Sensors*. 2017; 17(12):2778.
https://doi.org/10.3390/s17122778

**Chicago/Turabian Style**

Yang, Meng, Fei Wang, Yibin Wang, and Nanning Zheng. 2017. "A Denoising Method for Randomly Clustered Noise in ICCD Sensing Images Based on Hypergraph Cut and Down Sampling" *Sensors* 17, no. 12: 2778.
https://doi.org/10.3390/s17122778