# Hyperspectral Remote Sensing Images Deep Feature Extraction Based on Mixed Feature and Convolutional Neural Networks

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## Abstract

**:**

## 1. Introduction

_{SFMF-spa}and Two-CNN

_{fre-spe}, to jointly learn the SFMF-spatial and frequency spectrum-spectral features, respectively; a three-branch CNN, i.e., Three-CNN, to jointly learn the spectral-frequency spectrum-spatial features, and a combination of 3-D CNN and PCA (3-D CNN-PCA) to further extract joint SFMF-spatial features, the CNNs with different structures used in this paper is to verify the effectiveness of introducing frequency spectrum features. The following improvements are also made in this paper: (1) Considering that each frequency spectrum component reflects part of the overall character of a spectral pixel, and the traditional small convolution kernels in CNNs can only detect the local information, therefore a large full-size convolution kernel is used in the network branch fed with the frequency spectrum feature. (2) A pre-learning strategy is presented, i.e., the basic single branch CNN is used to pre-learn the weights of the branches of the multi-branch CNNs, which can avoid multi-branch CNNs from falling into a locally optimal solution to a certain extent and improve the training speed.

_{spe-spa}using the spectral and spatial features and that adding the presented frequency spectrum feature into CNNs can improve the terrain classification accuracy.

## 2. Proposed Pixel Frequency Spectrum Feature and Feature Mixing

#### 2.1. Proposed Pixel Frequency Spectrum Feature

#### 2.2. Proposed Spectral and Frequency Spectrum Mixed Feature

**m**by direct combination is

## 3. Proposed Multi-Branch CNN Models, 3-D CNN-PCA Model, and Training Strategy

#### 3.1. Basic CNN

#### 3.2. Proposed Multi-Branch CNNs

#### 3.2.1. Proposed Two-Branch CNNs

_{SFMF-spa}and Two-CNN

_{fre-spe}, to jointly learn the SFMF-spatial and frequency spectrum-spectral features, respectively. Shown in Figure 1 is the Two-CNN

_{SFMF-spa}whose two branches are fed into the presented SFMF and spatial feature respectively, each branch has l convolution and pooling layers and L fully connected layers.

_{fre-spe}whose two branches are fed with the presented frequency spectrum feature ${\mathit{f}}_{n}$ and the spectral pixel feature ${\mathit{s}}_{n}$ respectively. After l layers 1-D convolution and pooling operations, two branches respectively output features ${\mathit{x}}_{fre}^{l}({\mathit{f}}_{n})$ and ${\mathit{x}}_{spe}^{l}({\mathit{s}}_{n})$ which are mixed and fed into the fully connected layers, and the output of the first fully connected layer is

#### 3.2.2. Proposed Three-Branch CNN

#### 3.3. 3-D CNN-PCA

#### 3.4. Proposed Pre-Learning Strategy

## 4. Experiment Results

_{fre}), the experimental results of the basic CNN fed with spectral feature (CNN

_{spe}), basic CNN fed with the presented SFMF (CNN

_{SFMF}), presented Two-CNN

_{fre-spe}, presented Two-CNN

_{SFMF-spa}, Two-CNN fed with spectral and spatial features (Two-CNN

_{spe-spa}), presented 3-D CNN-PCA fed with the HRSIs containing SFMF feature (3-D CNN-PCA

_{SFMF-spa}), and 3-D CNN and PCA combination method fed with the original HRSI (3-D CNN-PCA

_{spe-spa}) are compared.

#### 4.1. Experiment Datasets

#### 4.2. CNNs Structure Design and Parameter Setting

#### 4.3. Effectiveness Analysis of Proposed Pre-Learning Training Strategy

#### 4.4. Classification Results

_{fre}are 1.7%, 1.33%, and 1.57% lower than those of CNN

_{spe}, which shows that the sole frequency spectrum feature is not better than the sole spectral feature; the AOA is increased 1.51, 1.01, and 0.67 percentage points by CNN

_{SFMF}respectively compared with CNN

_{spe}; the AOA is increased by 2.33, 1.93 and 1.76 percentage points by Two-CNN

_{fre-spe}respectively compared with CNN

_{spe}; the AOA is increased by 0.14, 0.38, and 0.01 percentage points by 3-D CNN-PCA

_{SFMF-spa}respectively compared with 3-D CNN-PCA

_{spe-spa}. Multi-branch CNNs fully use different features, and finally can obtain fusion deep features. By comparing the multi-branch CNNs fed with the spatial feature and 3-D CNN-PCA

_{spe-spa}, it is found that introducing the frequency spectrum feature can also obtain better classification accuracy. Comparing the SDs of the experimental results, we can see that the SDs of the experimental results obtained by the methods adding the presented frequency spectrum feature are smaller, indicating that the classification results of the methods adding the frequency spectrum feature are more stable. By comparing the computational cost of each model, it can be concluded that the addition of frequency spectrum features can improve the classification efficiency of the model and slightly increase the calculational cost of the model.

_{spe}and CNN

_{SFMF}methods under 5% training data of the Pavia University dataset. The diagonal value in the confusion matrix represents the number of pixels correctly classified in the testing data. Figure 7 shows that there are 964 more diagonal pixels in the confusion matrix of CNN

_{SFMF}which uses the presented spectral and frequency spectrum mixed feature than those in the confusion matrix of CNN

_{spe}which only uses the spectral feature. The area under the ROC curve can be used to indicate the classification efficiency of the model. The larger the area, the better the classification efficiency. Figure 8 shows that the area of the ROC curve of each class of CNN

_{SFMF}is larger than that of CNN

_{spe}.

_{fre}are 11.05, 10.91, and 8.91 percentage points lower than those of CNN

_{spe}; the AOAs of CNN

_{SFMF}are 2.62, 1.93, and 0.36 percentage points higher than those of CNN

_{spe}; the AOAs of Two-CNN

_{fre-spe}are 3.84, 2.20, and 1.81 percentage points higher than those of CNN

_{spe}; the AOAs of 3D-CNN-PCA

_{SFMF-spa}are 1.51, 0.26, and 0.07 percentage points higher than those of 3-D CNN-PCA

_{spe-spa}. By comparing with the multi-branch CNNs fed with the spatial feature, it is found that introducing the frequency spectrum feature obtains better classification accuracy.

_{spe}and CNN

_{SFMF}methods under the 5% training data of the Indian Pines dataset. Figure 9 shows that the confusion matrix of CNN

_{SFMF}has 247 more diagonal pixels than the confusion matrix of CNN

_{spe}. Figure 10 shows that the area of the ROC curve of each class of CNN

_{SFMF}is larger than that of CNN

_{spe}.

_{fre}are respectively 2.69%, 0.3%, and 1.42% less than those of CNN

_{spe}; the AOAs of CNN

_{SFMF}are respectively 1.20%, 1.98%, and 0.39% better than those of CNN

_{spe}; the AOAs of Two-CNN

_{fre-spe}are respectively 1.10%, 2.04%, and 1.28% better than those of CNN

_{spe}; the AOAs of 3-D CNN-PCA

_{SFMF-spa}are respectively 2.57%, 0.48%, and 0.02% better than those of 3-D CNN-PCA

_{spe-spa}. By comparing with the multi-branch CNNs fed with the spatial feature and 3-D CNN-PCA, it is found that introducing the frequency spectrum feature obtains better classification accuracy. We can see that the SDs of the experimental results of the methods adding the frequency spectrum feature are smaller than those of the other methods. It also can be seen that the addition of the frequency spectrum feature can improve the classification efficiency and slightly increase the computational cost.

_{spe}and CNN

_{SFMF}methods under the 5% training data of the Botswana dataset. Figure 11 shows that there are 98 more diagonal pixels in the confusion matrix of CNN

_{SFMF}than those in the confusion matrix of CNN

_{spe}. Figure 12 shows that the area of the ROC curve of each class of CNN

_{SFMF}is also larger than that of CNN

_{spe}.

#### 4.5. Discussion of Classification Results

_{spe}and Two-CNN

_{fre-spe}as examples, under 5%, 10% and 20% of the training samples, the classification accuracy of Two-CNN

_{fre-spe}is 2.62%, 2.00%, and 1.47% higher than that of CNN

_{spe}on average for the Indian Pines dataset, Pavia University dataset, and Botswana dataset, respectively. From the classification accuracies of different datasets under 5%, 10%, and 20% training data, it can be concluded that the addition of the frequency spectrum feature in the case of fewer training samples can generally improve the classification accuracy. However, compared with the other two datasets, the number of labeled samples in Botswana is too small, although the addition of the frequency spectrum feature increases the classification information, it also leads to some overfitting, which leads to a relatively small improvement in classification accuracy.

_{SFMF-spa}, Two-CNN

_{fre-spe}, and Three-CNN, based on pre-learning training strategy also get better classification results, this is because these multi-branch CNNs can extract more discriminative deep fusion features by employing several single branches of convolution and pooling layers. Compared with the ordinary CNNs methods using spectral pixel and spatial features, Two-CNN

_{SFMF-spa}and Three-CNN employ the spectral pixel, pixel frequency spectrum, and spatial features to get the deep fusion features with more discriminative information.

## 5. Conclusions

_{SFMF-spa}method is presented to verify the effectiveness of introducing frequency spectrum feature. The experimental results on three real HRSIs show that adding frequency spectrum feature into CNN can effectively improve the classification accuracy and the presented multi-branch CNNs and 3-D CNN-PCA

_{SFMF-spa}can extract more discriminative deep fusion features of HRSIs.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 6.**Comparison of different training strategies: (

**a**) Accuracy convergence speed and (

**b**) Loss convergence speed of Two-CNN

_{fre-spe}.

**Figure 7.**Comparison of confusion matrix under Pavia University 5% training data: (

**a**) CNN

_{spe}(

**b**) CNN

_{SFMF}.

**Figure 8.**Comparison of ROC curve under Pavia University 5% training data: (

**a**) CNN

_{spe}(

**b**) CNN

_{SFMF}.

**Figure 9.**Comparison of confusion matrix under Indian Pines 5% training data: (

**a**) CNN

_{spe}(

**b**) CNN

_{SFMF}.

**Figure 10.**Comparison of ROC curve under Indian Pines 5% training data: (

**a**) CNN

_{spe}(

**b**) CNN

_{SFMF}.

**Figure 11.**Comparison of confusion matrix under Botswana 5% training data: (

**a**) CNN

_{spe}(

**b**) CNN

_{SFMF}.

Layer Name | I1 | C2 S3 | C4 S5 | C6 S7 | C8 S9 | C10 S11 | F12 | F13 | O14 | ||
---|---|---|---|---|---|---|---|---|---|---|---|

Kernel Size | Pavia | Spectral/ SFMF | 1 × 103/ 1 × 206 | 1 × 8 1 × 2 | 1 × 7 1 × 2 | 1 × 8 1 × 2 | - | - | F | F | 1 × 9 |

Spatial | 21 × 21 | 3 × 3 2 × 2 | 3 × 3 2 × 2 | - | - | - | 1 × 9 | ||||

Fre. spectrum | 1 × 103 | 1 × 103 | - | - | - | - | 1 × 9 | ||||

SFMF-Spa. | 21 × 21 × 80 | 3 × 3 × 3 2 × 2 × 2 | 3 × 3 × 3 2 × 2 × 2 | - | - | - | 1 × 9 | ||||

Spectral-Spa. | 21 × 21 × 40 | 3 × 3 × 3 2 × 2 × 2 | 3 × 3 × 3 2 × 2 × 2 | - | - | - | 1 × 9 | ||||

Indian | Spectral/ SFMF | 1 × 220/ 1 × 440 | 1 × 5 1 × 2 | 1 × 5 1 × 2 | 1 × 4 1 × 2 | 1 × 5 1 × 2 | 1 × 4 1 × 2 | 1 × 16 | |||

Spatial | 21 × 21 | 3 × 3 2 × 2 | 3 × 3 2 × 2 | - | - | - | 1 × 16 | ||||

Fre. spectrum | 1 × 220 | 1 × 220 | - | - | - | - | 1 × 16 | ||||

SFMF-Spa. | 21 × 21 × 175 | 3 × 3 × 3 2 × 2 × 2 | 3 × 3 × 3 2 × 2 × 2 | - | - | - | 1 × 16 | ||||

Spectral-Spa. | 21 × 21 × 100 | 3 × 3 × 3 2 × 2 × 2 | 3 × 3 × 3 2 × 2 × 2 | - | - | - | 1 × 16 | ||||

Bot | Spectral/ SFMF | 1 × 145/ 1 × 290 | 1 × 8 1 × 2 | 1 × 7 1 × 2 | 1 × 8 1 × 2 | - | - | 1 × 14 | |||

Spatial | 21 × 21 | 3 × 3 2 × 2 | 3 × 3 2 × 2 | - | - | - | 1 × 14 | ||||

Fre. spectrum | 1 × 145 | 1 × 145 | - | - | - | - | 1 × 14 | ||||

SFMF-Spa. | 21 × 21 × 30 | 3 × 3 × 3 2 × 2 × 2 | 3 × 3 × 3 2 × 2 × 2 | - | - | - | 1 × 14 | ||||

Spectral-Spa. | 21 × 21 × 90 | 3 × 3 × 3 2 × 2 × 2 | 3 × 3 × 3 2 × 2 × 2 | - | - | - | 1 × 14 | ||||

FeatureMap | Pavia | Spectral/ SFMF | 1 | 6 | 12 | 24 | - | - | 256 | - | 9 |

Spatial | 1 | 30 | 30 | - | - | - | 400 | 400 | 9 | ||

Fre. spectrum | 1 | 103 | - | - | - | - | 256 | - | 9 | ||

SFMF-Spa. | 1 | 6 | 12 | - | - | - | 256 | - | 9 | ||

Spectral-Spa. | 1 | 6 | 12 | - | - | - | 256 | - | 9 | ||

Indian | Spectral/ SFMF | 1 | 6 | 12 | 24 | 48 | 96 | 256 | - | 16 | |

Spatial | 1 | 30 | 30 | - | - | - | 256 | 256 | 16 | ||

Fre. spectrum | 1 | 220 | - | - | - | - | 256 | - | 16 | ||

SFMF-Spa. | 1 | 6 | 12 | - | - | - | 256 | - | 16 | ||

Spectral-Spa. | 1 | 6 | 12 | - | - | - | 256 | - | 16 | ||

Bot | Spectral/ SFMF | 1 | 6 | 12 | 24 | - | - | 256 | - | 14 | |

Spatial | 1 | 6 | 12 | - | - | - | 256 | - | 14 | ||

Fre. spectrum | 1 | 145 | - | - | - | - | 256 | - | 14 | ||

SFMF-Spa. | 1 | 6 | 12 | - | - | - | 256 | - | 14 | ||

Spectral-Spa. | 1 | 6 | 12 | - | - | - | 256 | - | 14 |

Ratio of Training Samples | 5% | 10% | 20% | Computational Cost |
---|---|---|---|---|

AOA(%) ± SD(%) | AOA(%) ± SD(%) | AOA(%) ± SD(%) | ||

CNN_{fre} | 89.62 ± 0.42 | 91.73 ± 0.34 | 92.41 ± 0.29 | 2.19 M |

CNN_{spe} | 91.32 ± 1.32 | 93.06 ± 0.61 | 93.98 ± 0.50 | 5.74 M |

CNN_{SFMF} | 92.83 ± 0.70 | 94.07 ± 0.36 | 94.65 ± 0.36 | 22.32 M |

Two-CNN_{fre-spe} | 93.65 ± 0.03 | 94.99 ± 0.03 | 95.74 ± 0.03 | 21.39 M |

Two-CNN_{spe-spa} | 93.24 ± 0.30 | 96.36 ± 0.71 | 98.54 ± 0.34 | 111.44 M |

Two-CNN_{SFMF-spa} | 93.41 ± 0.13 | 96.73 ± 0.20 | 98.67 ± 0.05 | 228.41 M |

Three-CNN | 93.39 ± 0.16 | 96.62 ± 0.18 | 98.55 ± 0.22 | 122.63 M |

3-D CNN-PCA_{spe-spa} | 98.37 ± 0.20 | 98.74 ± 1.13 | 99.77 ± 0.06 | 910.15 M |

3-D CNN-PCA_{SFMF-spa} | 98.51 ± 0.20 | 99.12 ± 0.14 | 99.78 ± 0.05 | 3695.57 M |

Ratio of Training Samples | 5% | 10% | 20% | Computational Cost |
---|---|---|---|---|

AOA(%) ± SD(%) | AOA(%) ± SD(%) | AOA(%) ± SD(%) | ||

CNN_{fre} | 63.39 ± 0.21 | 70.31 ± 0.39 | 76.84 ± 0.57 | 21.30 M |

CNN_{spe} | 74.44 ± 1.28 | 81.22 ± 2.30 | 85.75 ± 1.46 | 18.44 M |

CNN_{SFMF} | 77.06 ± 1.64 | 83.15 ± 1.36 | 86.11 ± 0.82 | 68.71 M |

Two-CNN_{fre-spe} | 78.28 ± 0.24 | 83.42 ± 0.22 | 87.56 ± 0.31 | 125.48 M |

Two-CNN_{spe-spa} | 64.50 ± 1.16 | 85.91 ± 0.33 | 95.52 ± 0.35 | 238.18 M |

Two-CNN_{SFMF-spa} | 68.25 ± 0.20 | 87.87 ± 0.74 | 95.55 ± 0.29 | 502.88 M |

Three-CNN | 64.77 ± 1.19 | 86.01 ± 0.85 | 95.63 ± 0.14 | 345.22 M |

3-D CNN-PCA_{spe-spa} | 93.16 ± 0.42 | 97.37 ± 0.11 | 99.00 ± 0.17 | 5790.30 M |

3-D CNN-PCA_{SFMF-spa} | 94.67 ± 0.42 | 97.63 ± 0.25 | 99.07 ± 0.16 | 17,811.00 M |

Ratio of Training Samples | 5% | 10% | 20% | Computational Cost |
---|---|---|---|---|

AOA(%) ± SD(%) | AOA(%) ± SD(%) | AOA(%) ± SD(%) | ||

CNN_{fre} | 83.19 ± 0.29 | 89.09 ± 0.71 | 91.93 ± 0.17 | 6.10 M |

CNN_{spe} | 85.88 ± 1.47 | 89.39 ± 1.28 | 93.35 ± 0.62 | 11.28 M |

CNN_{SFMF} | 87.08 ± 0.41 | 91.37 ± 0.47 | 93.74 ± 0.75 | 43.40 M |

Two-CNN_{fre-spe} | 86.98 ± 0.29 | 91.43 ± 0.47 | 94.63 ± 0.26 | 42.14 M |

Two-CNN_{spe-spa} | 63.84 ± 0.71 | 84.59 ± 0.62 | 91.50 ± 0.37 | 40.21 M |

Two-CNN_{SFMF-spa} | 65.07 ± 0.75 | 84.87 ± 1.07 | 92.21 ± 0.29 | 100.59 M |

Three-CNN | 72.47 ± 1.42 | 85.17 ± 0.70 | 93.19 ± 0.28 | 71.06 M |

3-D CNN-PCA_{spe-spa} | 90.84 ± 0.87 | 98.15 ± 0.48 | 99.68 ± 0.20 | 4684.49 M |

3-D CNN-PCA_{SFMF-spa} | 93.41 ± 0.87 | 98.63 ± 0.44 | 99.70 ± 0.11 | 506.36 M |

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**MDPI and ACS Style**

Liu, J.; Yang, Z.; Liu, Y.; Mu, C.
Hyperspectral Remote Sensing Images Deep Feature Extraction Based on Mixed Feature and Convolutional Neural Networks. *Remote Sens.* **2021**, *13*, 2599.
https://doi.org/10.3390/rs13132599

**AMA Style**

Liu J, Yang Z, Liu Y, Mu C.
Hyperspectral Remote Sensing Images Deep Feature Extraction Based on Mixed Feature and Convolutional Neural Networks. *Remote Sensing*. 2021; 13(13):2599.
https://doi.org/10.3390/rs13132599

**Chicago/Turabian Style**

Liu, Jing, Zhe Yang, Yi Liu, and Caihong Mu.
2021. "Hyperspectral Remote Sensing Images Deep Feature Extraction Based on Mixed Feature and Convolutional Neural Networks" *Remote Sensing* 13, no. 13: 2599.
https://doi.org/10.3390/rs13132599