4.2.2. Spectral Information Recovery

To adapt to our partitioned extraction network structure and verify the effectiveness of spectral information recovery as well, we adopt the SA as the second evaluation criterion. The average SA curves of 7 band and 8 band test sets are shown in Figures 16 and 17, respectively. As seen below, we can find that the SA of the images reconstructed by the partitioned extraction algorithm is always smaller than that of JPEG2000, 3D-SPIHT and ResConv. Tables 2 and 3 list the detailed SA values of four representative test images of 7 band and 8 band, respectively. Supported by the chart and data below, it can be proven that the partitioned extraction algorithm obtains the smallest SA at all bit rates compared with the other three methods, and the smaller SA indicates that the images reconstructed by the proposed partitioned extraction method can obtain better spectral information recovery.

**Figure 16.** Average spectral angle (SA) curve of 7 band test images.


**Table 2.** SA of four 7 band test images (around a bit rate of 0.35).

**Figure 17.** Average SA curve of 8 band test images.

**Table 3.** SA of four 8 band test images (around a bit rate of 0.35).


#### **5. Conclusions**

In this paper, a novel end-to-end framework with partitioned extraction of spatial– spectral features for multispectral image compression is proposed. The algorithm pays close attention to the abundant spectral features of the multispectral images and is committed to preserving the integrity of the spectral–spatial features. The spectral and spatial feature modules extract corresponding features separately, after which the features are fused together for further processing. Likewise, the spectral and spatial features are severally recovered when reconstructing the images, which can help obtain images with high quality. To testify the validity of the framework, experiments are implemented on both 7 band and 8 band test sets. The results show that the proposed algorithm surpasses JPEG2000, 3D-SPIHT and ResConv on PSNR, visual effects and SA as well. The results on the 8 band show that the proposed method has achieved a more obvious superiority, which may prove that spectral information plays an indispensable role in multispectral image processing.

**Author Contributions:** All the authors made significant contributions to the work. Conceptualization, K.H. and S.Z.; methodology, F.K. and Y.L.; software, K.H.; validation, F.K. and K.H.; formal analysis, D.L.; investigation, F.K.; resources, F.K.; data curation, Y.L.; writing—original draft preparation, K.H.; writing—review and editing, F.K.; visualization, K.H.; supervision, F.K.; project administration, F.K.; funding acquisition, F.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China (grant no. 61801214), and National Key Laboratory Foundation (contract no. 6142411192112).

**Acknowledgments:** This research was supported by the National Natural Science Foundation of China and National Key Laboratory Foundation, and the authors are also grateful to the editor and reviewers for their constructive comments that helped to improve this work significantly.

**Conflicts of Interest:** The authors declare no conflict of interest and have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

#### **References**

