To evaluate the performance of the proposed APOCS-BM method, a series of experiments are performed on the Pavia and Jinyin Tan databases. All our experiments are done using MATLAB R2016b (Mathworks Corporation, MA, USA)on a 3.1 GHz Intel i5-2400 with 16GB RAM. The Pavia database consists of the Pavia University (PaviaU) scene and Pavia Centre (PaviaC) scene, which were captured by ROSIS sensor (German Aerospace Center (DLR), Cologne, Germany) during a flight campaign over Pavia in northern Italy. Part of the channels are removed due to noise; the number of spectral bands is 102 for PaviaC and 103 for PaviaU. The Jinyin Tan dataset is a scene of Jinyin Tan, a grassland located in Qinghai province, western China, which was captured by an airborne sensor named Lantian [
25,
26]. The number of spectral bands is 103. The image size of all HR used in the experiment is 256 × 256 pixels, which is part of the original dataset, and the image size of LR is 128 × 128 pixels. In order to evaluate the algorithm fairly, average peak signal noise ratio (A-PSNR), average structural similarity (A-SSIM) and spectral angle mapper (SAM) are employed as quality indexes. The A-PSNR and A-SSIM are calculated from the average value of whole spectral bands. The SAM represents the spectral distortion between the original and reconstructed HR image by absolute angles. The value of SAM should be zero when the reconstructed HR image is the same as the original. In the experiment, the proposed method is also compared with the linear interpolation method, DCT-based method [
10], Kim [
19], POCS [
17] and sparse representation-based SR (SR-SR) method [
20].
4.1. PaviaU and PaviaC Dataset
In the proposed APOCS-BM method, the original input is a single LR image (marked as LR image 1 in
Figure 3) with a size of
pixels. The first step of the proposed method is to obtain another three LR images (marked as LR image 1, LR image 2 and LR image 3 in
Figure 3), which are gained from the original input LR image convolving with a 5 × 5 Gaussian kernel of standard deviation 0.1, 0.2 and 0.5, respectively. Then, the four LR images are utilized to reconstruct the HR image. In the experiment, in order to achieve the universal property of the proposed method on different datasets, the patch size (
), iteration number (
) and
are all the same, where
,
and
.
(a) PaviaU dataset results
The other parameters used in the PaviaU dataset are:
,
.
Figure 4 shows the visual results of the PaviaU HSI dataset using different SRR methods. For the purpose of visualization by a human observer, the 80th, 28th and 9th spectral bands of the PaviaU dataset are chosen as the R, G and B channels of the color images in
Figure 4. It can be observed that the results gained by linear interpolation method or DCT-based method [
10] are blurrier than the others. The POSC [
17]-based results in
Figure 4e are over-sharpened, and the edges and corners are partly changed. From the visual comparison in
Figure 4, it can be seen that the proposed APOCS-BM method achieves better spatial-spectral information recovery than the other methods.
In order to further compare the results with other methods,
Figure 5a shows the spectral curves of reconstructed HR images (all spectral images). The horizontal axis is the spectral number, and the vertical axis is the gray value of the spectral image in the same coordinate (the coordinate located at (181,23), shown in
Figure 5c). The difference values between the reconstructed spectral curve and the original spectral curve are presented in
Figure 5b, the baseline represented by a black dotted line is the original spectral curve. It can be observed that the closer the spectral curves to the baseline, the better the result. From the comparison of different spectral curves in
Figure 5, the spectral curve reconstructed by the proposed APOCS-BM method is the best of all reconstructed spectral curves.
Table 1 shows the A-PSNR, A-SSIM and SAM of different reconstructed results. We can find that the proposed method has better performance than A-PSNR, A-SSIM and SAM.
(b) PaviaC dataset results
The parameters used in the PaviaC dataset are:
,
. The false color image of experimental results for the PaviaC dataset are shown in
Figure 6, and the spectral band numbers chosen to be the R, G and B channels are the same as PaviaU. The spectral curves with location (233, 163) are shown in
Figure 7. From the comparison of false color image and spectral curves, the reconstructed HR images via the proposed APOCS-BM method contain more spatial-spectral information than the other aforementioned methods. The mean difference value in
Figure 7b is smaller than the value in
Figure 5b, which is mainly caused by the different material properties. The A-PSNR, A-SSIM and SAM results are shown in
Table 2; similar to
Table 1, the proposed method performs the best in the different quality indexes.
4.2. Jinyin Tan Dataset
The Jinyin Tan dataset was captured by the airborne sensor Lantian [
21,
22]. The Jinyin Tan dataset 1 (the main scene is a water box) and Jinyin Tan dataset 2 (the main scene is grassland) comprise the Jinyin Tan dataset. The details are shown in
Figure 8, and the whole image size of the Jinyin Tan is
pixels. The 48th, 30th and 11th spectral bands in the Jinyin Tan dataset 1 are chosen as the R, G and B channels of the false color images in
Figure 8 and
Figure 9. The parameters used in the two datasets are:
,
, which have the best performance in the experiment.
and
affect the calculation of the adaptive threshold value
, which is used in APOCS. When
and
are increased, the adaptive threshold value is increased. In Algorithm 2’s Step 3.5, the amount of the pixel refreshed in
is decreased, but the accuracy of the constructed result (HR image) may be low. When these parameters are decreased, the amount of the pixel refreshed in
is increased, but the noise may be added through this increase. Therefore,
and
are different with different applications.
(a) Jinyin Tan dataset 1 (water box)
The false color images of experimental results for the Jinyin Tan dataset 1 are shown in
Figure 9, and the spectral curves with location (82, 184) are shown in
Figure 10. The difference value in
Figure 10b is much smaller than the values in
Figure 5b and
Figure 7b, which has a better reconstruction performance in the Jinyin Tan dataset 1. From the visual comparison in
Figure 9, we can see that the corners and image texture information of the water box obtained by the proposed method are much better than for the others. It also can be observed that the spatial-spectral information gained via the proposed method is closer to the original signals from
Figure 10.
Table 3 shows the A-PSNR, A-SSIM and SAM of different experimental results for the Jinyin Tan dataset 1. The A-PSNR in the proposed method is 44.7879, and the constructed HR image is really close to the original HR image. The SAM in the proposed method is 0.0411, which means the spectral distortion between the original and reconstructed HR image is really small. The quality indexes in
Table 3 prove that the proposed APOCS-BM method performs better than the others in the Jinyin Tan 1 dataset.
(b) Jinyin Tan dataset 2 (grassland)
Like the Jinyin Tan dataset 1, the false color images of experimental results for the Jinyin Tan dataset 2 are shown in
Figure 11, the spectral curves with location (182, 44) are shown in
Figure 12, and the quality indexes are shown in
Table 4. The 48th, 30th and 11th spectral bands are chosen as the R, G and B channels of the false color images in
Figure 11. It can be observed that the difference value in
Figure 12b is smaller than 2, and the reconstructed HR images in the Jinyin Tan dataset 2 have the best performance of difference value. From the comparison in the figures and quality indexes, we can see that the reconstructed HR images by the proposed method are much better than by the others, and the spatial-spectral information is well enhanced.
In the experiment, we also compared the execution times of different methods.
Table 5 shows the average execution time of different methods for the PaviaU dataset, PaviaC dataset, Jinyin Tan dataset 1 and Jinyin Tan dataset 2. The average execution time is for the reconstruction of a single HR image, not the whole spectral band. It can be observed that the average execution times in line interpolation, DCT-based method [
10] and Kim [
19] are close, and line interpolation is the fastest. However, the results gained by these methods do not perform well in the comparison of visual or spectral curves. The average execution times in the proposed method and POSC [
17] are close, but they are much slower than line interpolation method. The SR-SR method [
20] suffers the largest execution time, the main reason being the big dictionary used in the sparse coding and reconstruction. Considering the execution time and reconstruction accuracy of the HR image, the proposed method has the best performance.