# Application of Multiple-Optimization Filtering Algorithm in Remote Sensing Image Denoising

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## Abstract

**:**

## 1. Introduction

## 2. Principles and Methods of Filtering Algorithms

#### 2.1. Bilateral Filtering

#### 2.2. Canny Operator

#### 2.3. Differential Evolution Algorithm

## 3. Multiscale-Optimized Bilateral Filtering

_{i}represents the i-th sample data point.

- Edge preservation and smoothness control: The standard deviation of the Canny operator indicates the intensity variation in the edges of the image. By adjusting the size of the spatial domain Gaussian kernel based on the standard deviation of the Canny operator, the smoothness of the filter can be controlled. When the standard deviation of the Canny operator is larger, increasing the size of the spatial domain Gaussian kernel enhances the smoothing effect. In contrast, when the standard deviation of the Canny operator is smaller, reducing the size of the spatial domain Gaussian kernel helps preserve more details during the filtering process.
- Noise suppression: The convolution kernel size (D) of bilateral filtering can be used to control the degree of noise suppression. A larger convolution kernel can effectively average the neighboring pixel values and reduce the effect of noise. By dynamically adjusting the convolution kernel size based on the standard deviation and edge response width of the Canny operator, an optimal kernel size that aligns with the intensity of the noise can be adaptively selected, enabling superior noise suppression.
- High adaptability: The DE algorithm, which incorporates differential and mutation operations, enables a global search and the automatic selection of the optimal standard deviation for the pixel value color space based on the characteristics of the image. By considering the characteristics of the image, the DE algorithm selects the optimal standard deviation for the pixel value color space to adjust the pixel range domain kernel. This is achieved by combining it with the spatial domain Gaussian kernel and kernel size, enabling adaptive filtering.

## 4. Evaluation Criteria

#### 4.1. Mean Squared Error

#### 4.2. Structural Similarity Index

## 5. Experiment and Analysis

#### 5.1. GF-1 Image Simulation Experiment

#### 5.2. Unmanned Aerial Vehicle Image Simulation Experiment

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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Algorithm | PSNR/MES/SSIM | |||
---|---|---|---|---|

1% | 2% | 3% | 4% | |

AF | 33.147/31.502/0.889 | 32.739/34.605/0.872 | 32.395/37.456/0.856 | 32.119/39.917/0.844 |

AMF | 35.271/19.321/0.938 | 34.581/22.644/0.922 | 34.026/25.729/0.906 | 33.627/28.202/0.895 |

BF | 34.067/24.572/0.905 | 33.819/25.977/0.897 | 33.600/27.219/0.890 | 33.435/28.215/0.886 |

WD | 35.196/16.654/0.935 | 35.084/20.169/0.934 | 35.078/20.197/0.935 | 34.907/21.066/0.935 |

NLM | 34.468/21.634/0.920 | 34.014/23.895/0.909 | 33.621/26.072/0.900 | 33.321/27.723/0.893 |

MOBF | 38.937/8.300/0.976 | 38.048/10.190/0.965 | 37.362/11.937/0.957 | 36.876/13.348/0.951 |

Algorithm | PSNR/MSE/SSIM | |||
---|---|---|---|---|

1% | 2% | 3% | 4% | |

AF | 30.940/52.350/0.827 | 30.560/57.110/0.803 | 30.310/60.520/0.780 | 30.100/63.520/0.768 |

AMF | 32.440/37.040/0.889 | 31.950/41.470/0.868 | 31.640/44.590/0.853 | 31.400/47.060/0.839 |

BF | 33.320/28.650/0.921 | 33.050/30.090/0.918 | 32.880/32.210/0.918 | 32.760/31.990/0.920 |

WD | 34.390/23.630/0.949 | 34.340/23.890/0.950 | 34.090/25.320/0.950 | 34.080/25.370/0.949 |

NLM | 34.780/20.160/0.949 | 34.040/22.660/0.939 | 34.120/21.760/0.941 | 34.330/20.390/0.944 |

MOBF | 36.510/14.530/0.965 | 35.840/16.920/0.961 | 35.520/18.260/0.959 | 35.290/19.190/0.959 |

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**MDPI and ACS Style**

Zhang, X.; Li, Y.; Feng, X.; Hua, J.; Yue, D.; Wang, J.
Application of Multiple-Optimization Filtering Algorithm in Remote Sensing Image Denoising. *Sensors* **2023**, *23*, 7813.
https://doi.org/10.3390/s23187813

**AMA Style**

Zhang X, Li Y, Feng X, Hua J, Yue D, Wang J.
Application of Multiple-Optimization Filtering Algorithm in Remote Sensing Image Denoising. *Sensors*. 2023; 23(18):7813.
https://doi.org/10.3390/s23187813

**Chicago/Turabian Style**

Zhang, Xuelin, Yuan Li, Xiang Feng, Jian Hua, Dong Yue, and Jianxiong Wang.
2023. "Application of Multiple-Optimization Filtering Algorithm in Remote Sensing Image Denoising" *Sensors* 23, no. 18: 7813.
https://doi.org/10.3390/s23187813