# Multispectral Image Enhancement Based on the Dark Channel Prior and Bilateral Fractional Differential Model

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## Abstract

**:**

## 1. Introduction

- (1)
- By synthesizing the multiband information of multispectral remote sensing images, our algorithm obtains more accurate and clearer images than single-band remote sensing images.
- (2)
- A bilateral fractional differential model is firstly proposed and effectively improves the edge and textural details of multispectral images.
- (3)
- By expanding the bands and optimizing the transmittance of the dark channel prior model, an improved image with higher contrast and brightness is further obtained.

## 2. Related Work

- (1)
- The method of combining the dark channel prior algorithm with the fractional differential algorithm is applied to multispectral remote sensing image enhancement for the first time. Based on improving the overall brightness and detail characteristics of the image, the information of the spatial dimension and spectral dimension is combined to make full use of all wave bands of multispectral images.
- (2)
- Unlike the previous fractional differential algorithm, we propose a new fractional differential framework that enhances the edge and textural details of images. Considering the influence of the spatial distance on the pixel autocorrelation, we modify the fractional differential coefficients and propose the spatial domain fractional mask. Furthermore, according to the ability of the pixel similarity to judge the image edge, we propose the intensity domain fractional mask. Then the two above domains are fused to compose the bilateral fractional differential framework, and the enhanced images can be obtained by the framework. This framework can fully combine the information of spatial domain and intensity domain to maintain the details of the image in the smooth region and texture region and improve the image definition.
- (3)
- An improved dark channel prior algorithm, which extends the RGB channels to multiple channels and optimizes the transmittance through our proposed spatial domain fractional differentiation algorithm to make full use of the ground features of different spectral bands and enhance the overall brightness and contrast of an image, is proposed.

## 3. Proposed Method

#### 3.1. Dark Channel Prior

#### 3.2. Improved Dark Channel Prior

#### 3.3. G-L Fractional Differential Model

#### 3.4. Bilateral Fractional Differential Model

#### 3.4.1. Spatial Domain Fractional Differential Model

#### 3.4.2. Intensity Domain Fractional Differential Model

Algorithm 1. Multispectral image enhancement based on IDCP_BFD. | |

Input: A original multispectral image $R=\left\{{R}^{1},{R}^{2},\cdots ,{R}^{z}\right\}$ of the test dataset. | |

- (1)
**Improved Dark Channel Prior step:**- Through (13), the multispectral image
**R**is reverse as**I**to be used for the subsequent algorithm. - The enhanced multispectral image $J=\left\{{J}^{1},{J}^{2},\cdots ,{J}^{z}\right\}$ is generated via (14)–(22).
- (2)
**Bilateral Fractional Differential step:**
For λ = 1, to z doLet ${J}^{\lambda}$ be any bands in the multispectral image. | |

**Spatial domain Fractional Differential**- Enhance the ${J}^{\lambda}$ by using the spatial domain fractional differential normalized mask of Table 3.
- Implement histogram equalization and calculate the spatial domain enhanced image ${J}_{\alpha}^{\lambda \prime}$ via the (34).
| |

**Intensity domain Fractional Differential**- Enhance the ${J}^{\lambda}$ by using the intensity domain fractional differential normalized mask of Table 4.
- Perform contrast limited adaptive histogram equalization and calculate the intensity domain enhanced image ${J}_{\beta}^{\lambda \prime}$ via the (39).
| |

end for● Calculate the final enhanced image S by considering (40). Output: The enhanced result of the original image. |

## 4. Experimental Results and Analysis

_{k}represents the proportion of pixels with gray value k in the image. The larger the information entropy, the richer the information of the image.

#### 4.1. Dataset

#### 4.2. Parameter Analysis

#### 4.3. Comparative Experiments of Other Methods Based on Differential Filtering

#### 4.4. Comparative Experiments Based on Dark Channel Prior

#### 4.5. Comparative Experiments of Other Methods Based on Image Enhancement

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Original multispectral data 1: (

**a**) Band 1; (

**b**) Band 2; (

**c**) Band 3; (

**d**) Band 4; (

**e**) Band 5; (

**f**) Band 6; (

**g**) Band 7; (

**h**) 7-bands composite image.

**Figure 4.**Original multispectral data 2: (

**a**) Band 1; (

**b**) Band 2; (

**c**) Band 3; (

**d**) Band 4; (

**e**) Band 5; (

**f**) Band 6; (

**g**) Band 7; (

**h**) 7-bands composite image.

**Figure 5.**Original multispectral data 3: (

**a**) Band 1; (

**b**) Band 2; (

**c**) Band 3; (

**d**) Band 4; (

**e**) Band 5; (

**f**) Band 6; (

**g**) Band 7; (

**h**) 7-bands composite image.

**Figure 6.**Information entropy with different parameters in the multispectral image dataset: (

**a**) brightness adjustment parameter $K$; (

**b**) fractional differential order $v$.

**Figure 10.**The histograms corresponding to enhanced data 1 by using different input bands combinations: (

**a**) original DCP of 3-Bands; (

**b**) IDCP of 3-Bands; (

**c**) IDCP of 4-Bands; (

**d**) IDCP of 5-Bands; (

**e**) IDCP of 6-Bands; (

**f**) IDCP of 7-Bands.

**Figure 11.**The quantitative results of different input bands combinations used in 30 multispectral data: (

**a**) entropy; (

**b**) average gradient.

**Figure 12.**Enhanced image of data 2 by using: (

**a**) Retinex-Net; (

**b**) LIME; (

**c**) ACSEA; (

**d**) Proposed IDCP_BFD.

$0$ | $\frac{{v}^{2}-v}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{{v}^{2}-v}{2}$ |

$0$ | $-v$ | $0$ | $\frac{{v}^{2}-v}{2}$ | $-v$ | $1$ | $0$ | $-v$ | $0$ |

$0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $1$ | $0$ | $0$ |

**Table 2.**The 3 × 3 G-L fractional differential masks and 3 × 3 spatial domain fractional differential masks in (

**A**) negative x-direction; (

**B**) negative y-direction; (

**C**) upper-right diagonal direction.

(A) | |||||

$0$ | ${a}_{1}$ | $0$ | $\frac{{w}_{4}}{{w}_{3}+2{w}_{4}}{a}_{1}$ | $\frac{{w}_{3}}{{w}_{3}+2{w}_{4}}{a}_{1}$ | $\frac{{w}_{4}}{{w}_{3}+2{w}_{4}}{a}_{1}$ |

$0$ | ${a}_{0}$ | $0$ | $\frac{{w}_{2}}{3{w}_{1}+2{w}_{2}}{a}_{0}$ | $\frac{{w}_{1}}{3{w}_{1}+2{w}_{2}}{a}_{0}$ | $\frac{{w}_{2}}{3{w}_{1}+2{w}_{2}}{a}_{0}$ |

$0$ | $1$ | $0$ | $\frac{{w}_{1}}{3{w}_{1}+2{w}_{2}}{a}_{0}$ | $1$ | $\frac{{w}_{1}}{3{w}_{1}+2{w}_{2}}{a}_{0}$ |

(B) | |||||

$0$ | $0$ | $0$ | $\frac{{w}_{4}}{{w}_{3}+2{w}_{4}}{a}_{1}$ | $\frac{{w}_{2}}{3{w}_{1}+2{w}_{2}}{a}_{0}$ | $\frac{{w}_{1}}{3{w}_{1}+2{w}_{2}}{a}_{0}$ |

${a}_{1}$ | ${a}_{0}$ | $1$ | $\frac{{w}_{3}}{{w}_{3}+2{w}_{4}}{a}_{1}$ | $\frac{{w}_{1}}{3{w}_{1}+2{w}_{2}}{a}_{0}$ | $1$ |

$0$ | $0$ | $0$ | $\frac{{w}_{4}}{{w}_{3}+2{w}_{4}}{a}_{1}$ | $\frac{{w}_{2}}{3{w}_{1}+2{w}_{2}}{a}_{0}$ | $\frac{{w}_{1}}{3{w}_{1}+2{w}_{2}}{a}_{0}$ |

(C) | |||||

$0$ | $0$ | ${a}_{1}$ | $\frac{{w}_{3}{a}_{1}}{2{w}_{3}+2{w}_{4}+{w}_{5}}$ | $\frac{{w}_{4}{a}_{1}}{2{w}_{3}+2{w}_{4}+{w}_{5}}$ | $\frac{{w}_{5}{a}_{1}}{2{w}_{3}+2{w}_{4}+{w}_{5}}$ |

$0$ | ${a}_{0}$ | $0$ | $\frac{{w}_{1}{a}_{0}}{2{w}_{1}+{w}_{2}}$ | $\frac{{w}_{2}{a}_{0}}{2{w}_{1}+{w}_{2}}$ | $\frac{{w}_{4}{a}_{1}}{2{w}_{3}+2{w}_{4}+{w}_{5}}$ |

$1$ | $0$ | $0$ | $1$ | $\frac{{w}_{1}{a}_{0}}{2{w}_{1}+{w}_{2}}$ | $\frac{{w}_{3}{a}_{1}}{2{w}_{3}+2{w}_{4}+{w}_{5}}$ |

$\frac{{w}_{5}}{2{w}_{3}+2{w}_{4}+{w}_{5}}{a}_{2}$ | $\left(\frac{{w}_{4}}{2{w}_{3}+2{w}_{4}+{w}_{5}}+\frac{{w}_{4}}{{w}_{3}+2{w}_{4}}\right){a}_{2}$ | $\left(\frac{2{w}_{3}}{2{w}_{3}+2{w}_{4}+{w}_{5}}+\frac{{w}_{3}}{{w}_{3}+2{w}_{4}}\right){a}_{2}$ | $\left(\frac{{w}_{4}}{2{w}_{3}+2{w}_{4}+{w}_{5}}+\frac{{w}_{4}}{{w}_{3}+2{w}_{4}}\right){a}_{2}$ | $\frac{{w}_{5}}{2{w}_{3}+2{w}_{4}+{w}_{5}}{a}_{2}$ |

$\left(\frac{{w}_{4}}{2{w}_{3}+2{w}_{4}+{w}_{5}}+\frac{{w}_{4}}{{w}_{3}+2{w}_{4}}\right){a}_{2}$ | $\left(\frac{{w}_{2}}{2{w}_{1}+{w}_{2}}+\frac{2{w}_{2}}{3{w}_{1}+2{w}_{2}}\right){a}_{1}$ | $\left(\frac{2{w}_{1}}{2{w}_{1}+{w}_{2}}+\frac{3{w}_{1}}{3{w}_{1}+2{w}_{2}}\right){a}_{1}$ | $\left(\frac{{w}_{2}}{2{w}_{1}+{w}_{2}}+\frac{2{w}_{2}}{3{w}_{1}+2{w}_{2}}\right){a}_{1}$ | $\left(\frac{{w}_{4}}{2{w}_{3}+2{w}_{4}+{w}_{5}}+\frac{{w}_{4}}{{w}_{3}+2{w}_{4}}\right){a}_{2}$ |

$\left(\frac{2{w}_{3}}{2{w}_{3}+2{w}_{4}+{w}_{5}}+\frac{{w}_{3}}{{w}_{3}+2{w}_{4}}\right){a}_{2}$ | $\left(\frac{2{w}_{1}}{2{w}_{1}+{w}_{2}}+\frac{3{w}_{1}}{3{w}_{1}+2{w}_{2}}\right){a}_{1}$ | $8{a}_{0}$ | $\left(\frac{2{w}_{1}}{2{w}_{1}+{w}_{2}}+\frac{3{w}_{1}}{3{w}_{1}+2{w}_{2}}\right){a}_{1}$ | $\left(\frac{2{w}_{3}}{2{w}_{3}+2{w}_{4}+{w}_{5}}+\frac{{w}_{3}}{{w}_{3}+2{w}_{4}}\right){a}_{2}$ |

$\left(\frac{{w}_{4}}{2{w}_{3}+2{w}_{4}+{w}_{5}}+\frac{{w}_{4}}{{w}_{3}+2{w}_{4}}\right){a}_{2}$ | $\left(\frac{{w}_{2}}{2{w}_{1}+{w}_{2}}+\frac{2{w}_{2}}{3{w}_{1}+2{w}_{2}}\right){a}_{1}$ | $\left(\frac{2{w}_{1}}{2{w}_{1}+{w}_{2}}+\frac{3{w}_{1}}{3{w}_{1}+2{w}_{2}}\right){a}_{1}$ | $\left(\frac{{w}_{2}}{2{w}_{1}+{w}_{2}}+\frac{2{w}_{2}}{3{w}_{1}+2{w}_{2}}\right){a}_{1}$ | $\left(\frac{{w}_{4}}{2{w}_{3}+2{w}_{4}+{w}_{5}}+\frac{{w}_{4}}{{w}_{3}+2{w}_{4}}\right){a}_{2}$ |

$\frac{{w}_{5}}{2{w}_{3}+2{w}_{4}+{w}_{5}}{a}_{2}$ | $\left(\frac{{w}_{4}}{2{w}_{3}+2{w}_{4}+{w}_{5}}+\frac{{w}_{4}}{{w}_{3}+2{w}_{4}}\right){a}_{2}$ | $\left(\frac{2{w}_{3}}{2{w}_{3}+2{w}_{4}+{w}_{5}}+\frac{{w}_{3}}{{w}_{3}+2{w}_{4}}\right){a}_{2}$ | $\left(\frac{{w}_{4}}{2{w}_{3}+2{w}_{4}+{w}_{5}}+\frac{{w}_{4}}{{w}_{3}+2{w}_{4}}\right){a}_{2}$ | $\frac{{w}_{5}}{2{w}_{3}+2{w}_{4}+{w}_{5}}{a}_{2}$ |

$\frac{{\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(2,-2\right)}}{\sum {\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(i,j\right)}}{a}_{2}$ | $\frac{{\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(2,-1\right)}}{\sum {\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(i,j\right)}}{a}_{2}$ | $\frac{{\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(2,0\right)}}{\sum {\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(i,j\right)}}{a}_{2}$ | $\frac{{\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(2,1\right)}}{\sum {\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(i,j\right)}}{a}_{2}$ | $\frac{{\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(2,2\right)}}{\sum {\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(i,j\right)}}{a}_{2}$ |

$\frac{{\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(1,-2\right)}}{\sum {\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(i,j\right)}}{a}_{2}$ | $\frac{{\mathrm{w}}_{p{\mathsf{\Omega}}_{1}\left(1,-1\right)}}{\sum {\mathrm{w}}_{p{\mathsf{\Omega}}_{1}\left(i,j\right)}}{a}_{1}$ | $\frac{{\mathrm{w}}_{p{\mathsf{\Omega}}_{1}\left(1,0\right)}}{\sum {\mathrm{w}}_{p{\mathsf{\Omega}}_{1}\left(i,j\right)}}{a}_{1}$ | $\frac{{\mathrm{w}}_{p{\mathsf{\Omega}}_{1}\left(1,1\right)}}{\sum {\mathrm{w}}_{p{\mathsf{\Omega}}_{1}\left(i,j\right)}}{a}_{1}$ | $\frac{{\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(1,2\right)}}{\sum {\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(i,j\right)}}{a}_{2}$ |

$\frac{{\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(0,-2\right)}}{\sum {\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(i,j\right)}}{a}_{2}$ | $\frac{{\mathrm{w}}_{p{\mathsf{\Omega}}_{1}\left(0,-1\right)}}{\sum {\mathrm{w}}_{p{\mathsf{\Omega}}_{1}\left(i,j\right)}}{a}_{1}$ | ${\mathrm{w}}_{p\left(0,0\right)}{a}_{0}$ | $\frac{{\mathrm{w}}_{p{\mathsf{\Omega}}_{1}\left(0,1\right)}}{\sum {\mathrm{w}}_{p{\mathsf{\Omega}}_{1}\left(i,j\right)}}{a}_{1}$ | $\frac{{\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(0,2\right)}}{\sum {\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(i,j\right)}}{a}_{2}$ |

$\frac{{\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(-1,-2\right)}}{\sum {\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(i,j\right)}}{a}_{2}$ | $\frac{{\mathrm{w}}_{p{\mathsf{\Omega}}_{1}\left(-1,-1\right)}}{\sum {\mathrm{w}}_{p{\mathsf{\Omega}}_{1}\left(i,j\right)}}{a}_{1}$ | $\frac{{\mathrm{w}}_{p{\mathsf{\Omega}}_{1}\left(-1,0\right)}}{\sum {\mathrm{w}}_{p{\mathsf{\Omega}}_{1}\left(i,j\right)}}{a}_{1}$ | $\frac{{\mathrm{w}}_{p{\mathsf{\Omega}}_{1}\left(-1,1\right)}}{\sum {\mathrm{w}}_{p{\mathsf{\Omega}}_{1}\left(i,j\right)}}{a}_{1}$ | $\frac{{\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(-1,2\right)}}{\sum {\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(i,j\right)}}{a}_{2}$ |

$\frac{{\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(-2,-2\right)}}{\sum {\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(i,j\right)}}{a}_{2}$ | $\frac{{\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(-2,-1\right)}}{\sum {\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(i,j\right)}}{a}_{2}$ | $\frac{{\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(-2,0\right)}}{\sum {\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(i,j\right)}}{a}_{2}$ | $\frac{{\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(-2,1\right)}}{\sum {\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(i,j\right)}}{a}_{2}$ | $\frac{{\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(-2,2\right)}}{\sum {\mathrm{w}}_{p{\mathsf{\Omega}}_{2}\left(i,j\right)}}{a}_{2}$ |

Original Images | Metrics | ||||
---|---|---|---|---|---|

μ | C | H | AG | ||

Data 1 | Band1 | 113.73 | 50.06 | 5.54 | 4.33 |

Band2 | 59.25 | 21.06 | 5.06 | 2.91 | |

Band3 | 71.15 | 44.76 | 5.68 | 4.24 | |

Band4 | 72.48 | 41.51 | 5.47 | 4.07 | |

Band5 | 115.07 | 116.69 | 6.54 | 6.94 | |

Band6 | 190.00 | 1.47 | 4.81 | 0.73 | |

Band7 | 69.97 | 55.95 | 6.03 | 4.83 | |

Data 2 | Band1 | 115.15 | 50.06 | 5.73 | 4.37 |

Band2 | 59.21 | 19.70 | 5.19 | 2.85 | |

Band3 | 69.62 | 42.37 | 5.83 | 4.18 | |

Band4 | 74.93 | 47.92 | 5.91 | 4.36 | |

Band5 | 111.22 | 109.63 | 6.65 | 6.84 | |

Band6 | 187.27 | 2.01 | 5.07 | 0.85 | |

Band7 | 67.38 | 56.89 | 6.20 | 4.91 | |

Data 3 | Band1 | 88.51 | 25.78 | 5.50 | 3.30 |

Band2 | 45.43 | 11.72 | 4.91 | 2.19 | |

Band3 | 49.57 | 33.09 | 5.56 | 3.57 | |

Band4 | 80.82 | 95.66 | 6.39 | 6.04 | |

Band5 | 92.72 | 60.55 | 5.88 | 4.98 | |

Band6 | 171.47 | 2.62 | 5.62 | 0.95 | |

Band7 | 50.89 | 43.52 | 5.86 | 4.18 | |

Average in 30 multispectral data | Band1 | 97.84 | 34.04 | 5.61 | 3.79 |

Band2 | 51.12 | 15.94 | 5.07 | 2.61 | |

Band3 | 59.92 | 39.95 | 5.76 | 4.08 | |

Band4 | 76.11 | 52.51 | 5.92 | 4.48 | |

Band5 | 106.76 | 93.46 | 6.37 | 6.27 | |

Band6 | 174.41 | 2.24 | 5.12 | 0.86 | |

Band7 | 61.53 | 53.72 | 6.04 | 4.73 |

Test Images | Methods | Metrics | ||||
---|---|---|---|---|---|---|

μ | C | H | AG | Time(s) | ||

Data 1 | Sobel | 87.68 | 121.56 | 6.06 | 5.74 | 2.21 |

Laplacian | 96.13 | 2530.04 | 7.19 | 32.68 | 2.15 | |

Yipufei [19] | 96.13 | 2270.00 | 7.17 | 30.85 | 2.14 | |

MGL [20] | 96.13 | 2090.31 | 7.13 | 29.81 | 2.22 | |

Wadhwa et al. [21] | 96.02 | 95.72 | 5.97 | 5.47 | 7.24 | |

Proposed BFD | 114.69 | 3202.81 | 7.55 | 40.53 | 6.67 | |

Data 2 | Sobel | 97.10 | 108.57 | 6.12 | 5.67 | 2.24 |

Laplacian | 105.90 | 2311.94 | 7.22 | 31.72 | 2.09 | |

Yipufei [19] | 105.90 | 2063.72 | 7.20 | 29.92 | 2.21 | |

MGL [20] | 105.90 | 1899.01 | 7.15 | 28.90 | 2.18 | |

Wadhwa et al. [21] | 105.74 | 91.62 | 6.01 | 5.34 | 7.24 | |

Proposed BFD | 120.37 | 3090.68 | 7.56 | 40.22 | 6.72 | |

Data 3 | Sobel | 75.20 | 102.33 | 5.80 | 4.81 | 2.23 |

Laplacian | 83.70 | 1372.77 | 6.82 | 24.18 | 2.16 | |

Yipufei [19] | 83.70 | 1227.02 | 6.79 | 22.75 | 2.21 | |

MGL [20] | 83.70 | 1145.76 | 6.76 | 22.19 | 2.14 | |

Wadhwa et al. [21] | 83.54 | 54.96 | 5.69 | 4.23 | 7.15 | |

Proposed BFD | 106.19 | 2160.91 | 7.23 | 32.92 | 6.65 | |

Average in 30 multispectral data | Sobel | 84.78 | 117.11 | 6.02 | 5.73 | 2.24 |

Laplacian | 93.75 | 2054.57 | 7.11 | 30.07 | 2.16 | |

Yipufei [19] | 93.75 | 1842.40 | 7.09 | 28.41 | 2.21 | |

MGL [20] | 93.75 | 1703.19 | 7.05 | 27.52 | 2.16 | |

Wadhwa et al. [21] | 93.56 | 89.58 | 5.98 | 5.28 | 7.22 | |

Proposed BFD | 112.21 | 2866.97 | 7.49 | 38.71 | 6.67 |

Test Images | Methods | Metrics | ||||
---|---|---|---|---|---|---|

μ | C | H | AG | Time(s) | ||

Data 2 | Retinex-Net | 160.20 | 51.46 | 4.95 | 3.83 | 2.82 |

LIME | 199.94 | 151.33 | 6.39 | 7.88 | 2.43 | |

ACSEA | 149.04 | 64.35 | 6.27 | 5.22 | 434.29 | |

Proposed | 120.37 | 3090.68 | 7.56 | 40.22 | 6.72 | |

Average in 30 multispectral data | Retinex-Net | 159.43 | 54.43 | 4.87 | 3.83 | 2.73 |

LIME | 196.01 | 146.38 | 6.36 | 7.76 | 2.29 | |

ACSEA | 161.09 | 99.05 | 6.34 | 6.52 | 450.71 | |

Proposed | 112.21 | 2866.97 | 7.49 | 38.71 | 6.67 |

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## Share and Cite

**MDPI and ACS Style**

Chen, W.; Jia, Z.; Yang, J.; Kasabov, N.K.
Multispectral Image Enhancement Based on the Dark Channel Prior and Bilateral Fractional Differential Model. *Remote Sens.* **2022**, *14*, 233.
https://doi.org/10.3390/rs14010233

**AMA Style**

Chen W, Jia Z, Yang J, Kasabov NK.
Multispectral Image Enhancement Based on the Dark Channel Prior and Bilateral Fractional Differential Model. *Remote Sensing*. 2022; 14(1):233.
https://doi.org/10.3390/rs14010233

**Chicago/Turabian Style**

Chen, Weijie, Zhenhong Jia, Jie Yang, and Nikola K. Kasabov.
2022. "Multispectral Image Enhancement Based on the Dark Channel Prior and Bilateral Fractional Differential Model" *Remote Sensing* 14, no. 1: 233.
https://doi.org/10.3390/rs14010233