*4.1. Experimental Setup*

The proposed STF method is tested on four public hyperspectral datasets, which are shown in Table 1. Table 1 summarizes their characteristic.



**Table 1.** Characteristic of the four used datasets.

Pavia University dataset, Moffett field dataset, and Washington DC dataset are semi-synthetic dataset. Given a reference high spatial resolution HS image, the simulated low spatial resolution HS image and the simulated PAN image are generated. The simulated PAN image is generated by averaging the bands of the visible range of the reference image. According to the Wald's protocol [46], the low spatial resolution HS image is simulated by applying a 9 × 9 Gaussian kernel blurring and downsampling to the reference HS image, and the downsampling factor is 5. Hyperion dataset is a real dataset to evaluate the capability of the proposed method in real hyperspectral remote sensing image.

The proposed method is compared with six hyperspectral pansharpening methods, namely MTF-GLP with High Pass Modulation (MTF-GLP-HPM) [27], Bayesian sparsity promoted Gaussian prior (Bayesian Sparse) [30], constrained nonnegative matrix factorization (CNMF) [35], guided filter PCA (GFPCA) [38], Brovey transform (BT) [20] and principal component analysis (PCA) [15]. MTF-GLP-HPM (abbreviated as MGH) belongs to multiresolution analysis (MRA) class. Bayesian Sparse fusion method (abbreviated as BSF) is one of the Bayesian methods. The CNMF algorithm and the GFPCA fusion approach belong to matrix factorization based methods and hybrid methods, respectively. These four methods which give the state-of-the-art fusion performance were all presented in recent years. The BT and PCA method which are the simple and classical fusion methods belong to component substitution (CS) family. These compared methods cover the recent effective works and the existing five categories which have been described in introduction section. In the experiments, the number of endmembers is set to 20 for the CNMF approach. For the GFPCA algorithm, the window size and the blur degree of the guided filter are set to 17 and 10−<sup>6</sup> respectively. The pixel values of every test image are normalized to the range of 0–1.0 to reduce the amount of calculation.

To assess the capability of the proposed fusion method, several widely used evaluation indices are adopted, i.e., cross correlation (CC) [47], spectral angle mapper (SAM) [47], root mean squared error (RMSE), and erreur relative global adimensionnelle de synthse (ERGAS) [48]. CC is a spatial index and the best value is 1. SAM measures the degree of spectral similarity. The RMSE and ERGAS indices show the global quality of the fused image. The optimal value of SAM, RMSE, and ERGAS are 0. The experiments for the four datasets were all performed using MATLAB R2015b, and tested on a PC with an Intel Core i5-7300HQ CPU @ 2.50 GHz and 8 GB memory.

#### *4.2. Tradeoff Parameter Setting*

In the proposed method, the complete spatial details are finally included into the interpolated HS image. In order to reduce the spatial distortion, we define the tradeoff parameter *τ* to control the amount of the injected spatial details. The setting of the tradeoff parameter *τ* has an important impact on the spatial quality. Since the tradeoff parameter regulates the spatial distortion, the best value of *τ* can be chosen via the spatial index. Thus, for the sake of concluding the influence of *τ*, the proposed approach is tested on the Moffett field dataset and the Washington DC dataset to observe the CC values with different *τ* settings. Figure 4 shows the CC index values with different tradeoff parameter settings. When the tradeoff parameter *τ* is set to 0.1, the proposed method acquires the optimal CC

values. We have also performed on numerous hyperspectral remote sensing images, and discovered that *τ* = 0.1 also provides the largest CC values. Therefore, for the proposed method, the tradeoff parameter *τ* is set as 0.1.

**Figure 4.** CC values with different tradeoff parameter settings.

#### *4.3. Experiments on Simulated Hyperspectral Remote Sensing Datasets*

In this part, the experiments are performed on three simulated hyperspectral remote sensing datasets to evaluate the fusion performance of the proposed method. Three datasets are Pavia University dataset, Moffett field dataset, and Washington DC dataset, respectively.

#### 4.3.1. Pavia University Dataset

Figure 5a shows the reference high resolution HS image of Pavia University dataset. Figure 5d–j shows the fused HS images of each method for the Pavia University dataset. By comparing the fused images with the reference HS image visually, it can be observed that the GFPCA method looks blurry. This is because the GFPCA method utilizes the guided filter to transfer the spatial details from the PAN image to the HS image, but the spatial details are injected insufficiently. The BT approach provides enough spatial information, but the fused image obtained by the BT approach has spectral distortion in some areas, such as the trees and roads. Although the CNMF method has good fidelity of the spectral information, the CNMF method has deficient improvement of the spatial quality in some marginal areas, such as the edges of the trees and roofs. By contrast, we find that the PCA, BSF, MGH, and proposed STF method have the satisfactory fusion performance, and the MGH and STF methods achieve the better capability in preserving the spectral information compared with the PCA and BSF methods. In order to further compare the fusion performance, Figure 6 shows the error images (absolute values) of the competing methods for Pavia University dataset. Yellow means large differences, and blue means small differences. From Figure 6, it can be seen that the proposed SFT method shows the smallest differences between the fused HS image and the reference HS image.

Quantitative results of different fusion methods are shown in Table 2, which indicates that the proposed method achieves the best performance. The SAM, RMSE, and ERGAS values of the proposed method are the best, and the CC value of the proposed method is the second best. These results demonstrate that the proposed STF algorithm performs well in both the objective and subjective evaluations.

*Remote Sens.* **2018**, *10*, 373

**Figure 5.** Fusion results obtained by each method for Pavia University dataset. (**a**) Reference HS image; (**b**) Simulated PAN image; (**c**) Interpolated HS image; (**d**) PCA; (**e**) GFPCA; (**f**) BT; (**g**) CNMF; (**h**) BSF; (**i**) MGH; (**j**) STF.

**Figure 6.** Error images of the competing methods for Pavia University dataset. (**a**) PCA; (**b**) GFPCA; (**c**) BT; (**d**) CNMF; (**e**) BSF; (**f**) MGH; (**g**) STF.

**Table 2.** Quantitative results of different fusion methods for Pavia University dataset.


#### 4.3.2. Moffett Field Dataset

The fusion results obtained by each method for Moffett field dataset are displayed in Figure 7d–j. Visually, the PCA and BT methods have high fidelity in rendering the spatial details, but cause spectral distortion. This is due to the mismatching between the PAN image and the replaced spatial component. Compared with the PCA and BT approaches, the GFPCA seems to have less spectral distortion, but the spatial details are not sufficient. The fused result obtained by the CNMF method has good

spectral fidelity, but the edges and spatial structures are not sharp enough, especially in the rural areas. The visual analysis shows that the BSF, MGH, and STF methods give the better fused results. The MGH, and STF algorithms are clearer, especially in the rural regions and rivers. However, the pansharpened image obtained by the MGH approach is too sharp in some areas, such as the tall buildings in urban areas. By contrast, the proposed STF method has superior performance in terms of providing the spatial information while preserving the spectral information. Table 3 reports the objective quantitative results for each method. From Table 3, we can apparently see that the proposed STF method has the largest CC value, and smallest SAM, RMSE, and ERGAS values.

**Figure 7.** Fusion results obtained by each method for Moffett field dataset. (**a**) Reference HS image; (**b**) Simulated PAN image; (**c**) Interpolated HS image; (**d**) PCA; (**e**) GFPCA; (**f**) BT; (**g**) CNMF; (**h**) BSF; (**i**) MGH; (**j**) STF.

**Table 3.** Quantitative results of different fusion methods for Moffett field dataset.


The spectral reflectance curve difference values between the reference image and each fused image on one single pixel are compared to assess the spectral preservation performance. Figure 8 shows the spectral reflectance difference values on four pixels which are marked in yellow in Figure 7a. As shown in Figure 8, a gray dotted line is served as the benchmark. The closer the spectral reflectance difference values between the reference image and the fused image ge<sup>t</sup> to the dotted line, the more the spectral information is preserved. From Figure 8, it can be observed that the spectral reflectance difference values of the proposed method are most approximate to the dotted line (benchmark line) on the whole. These results validate the proposed method has the smallest difference when compared to other fusion methods.

**Figure 8.** Spectral reflectance difference values comparison on four single pixels shown in Figure 7a.

#### 4.3.3. Washington DC Dataset

The visual experimental results obtained by each method for the Washington DC dataset are shown in Figure 9d–j. In spite of good spatial quality, the fused images produced by the PCA and BT approaches cause spectral distortion in the roads and buildings. According to visual comparison of these results, the fused image generated by the MGH method has good fidelity of the spectral information. However, the MGH method suffers from spectral distortion in some areas, such as the roof areas. Compared with the PCA and MGH methods, the GFPCA algorithm has less spectral distortion. But the result of the GFPCA method has insufficient enhancement in the spatial aspect, and the fused image is blurry. The BSF, and STF method provide more spatial details compared to the CNMF method, since the CNMF method loses a little spatial information in the edges, such as in the roads and buildings. In contrast, the BSF, and STF method enhance more spatial information while preserving the spectral information of the original HS image.

**Figure 9.** Fusion results obtained by each method for Washington DC dataset. (**a**) Reference HS image; (**b**) Simulated PAN image; (**c**) Interpolated HS image; (**d**) PCA; (**e**) GFPCA; (**f**) BT; (**g**) CNMF; (**h**) BSF; (**i**) MGH; (**j**) STF.

To further compare the fusion capability, the error images (absolute values) of different approaches for the Washington DC dataset are shown in Figure 10. Yellow means large differences, and blue means small differences. As shown in Figure 10, the SFT method shows the smallest differences in most regions, which testifies the preeminent fusion performance of the proposed method. The values of objective quality evaluation of each method for the Washington DC dataset are tabulated in Table 4. As shown in Table 4, for the proposed method, the CC, SAM, and RMSE values are the best, which prove once again that the proposed method is superior to the compared hyperspectral pansharpening methods.

**Figure 10.** Error images of the competing methods for Washington DC dataset. (**a**) PCA; (**b**) GFPCA; (**c**) BT; (**d**) CNMF; (**e**) BSF; (**f**) MGH; (**g**) STF.


**Table 4.** Quantitative results of different fusion methods for Washington DC dataset.

#### *4.4. Experiments on Real Hyperspectral Remote Sensing Datasets*

In this part, the experiments are performed on the real hyperspectral remote sensing dataset to assess the fusion capability of the proposed method. The real HS dataset is the Hyperion dataset. Figure 11a,b show the low spatial resolution original HS image and the high spatial resolution PAN image. The fusion results of the competing methods are shown in Figure 11d–j. By a visual comparison of the pansharpened images, the PCA method has significant spectral distortion. For the GFPCA method, the spatial details are injected insufficiently, and the fused HS image looks fuzzy. The BSF method is better than the PCA method in preserving the spectral information, while the spatial details is a little less in the regard to some regions, such as the roads and grass. By contrast, the BT, CNMF, MGH, and STF method achieve the superior property. Since the low spatial resolution original HS image is unclear, the spectral information of the BT, CNMF, MGH, and STF method cannot accurately be compared. In the spatial aspect, the proposed STF method has the better performance, since it adds more spatial details.

**Figure 11.** Fusion results obtained by each method for Hyperion dataset. (**a**) HS image; (**b**) PAN image; (**c**) Interpolated HS image; (**d**) PCA; (**e**) GFPCA; (**f**) BT; (**g**) CNMF; (**h**) BSF; (**i**) MGH; (**j**) STF.

For the real HS dataset, a reference high spatial resolution HS image is commonly not available. The original low resolution HS image can be served as the reference image. According to the Wald's protocol [45], the available original HS image is degraded to generate a degraded HS image. The available PAN image is also degraded to obtain a degraded PAN image. The degraded HS and PAN images are fused by each method to obtain the fusion results. These fusion results are compared to the original HS image to evaluate the objective fusion performance of different methods. Table 5 reports the objective fusion results for each method. From Table 5, we can apparently see that the proposed STF has the largest CC value, and smallest SAM and ERGAS values. These results demonstrate that the proposed algorithm obtains the excellent fusion performance.


**Table 5.** Quantitative results of different fusion methods for Hyperion dataset.
