# A Probabilistic Hyperspectral Imagery Restoration Method
## 5 Experimental Results and Analysis
### Performance Evaluation on Simulated Noisy Dataset  
When we apply HSI restoration methods on real noisy data, we can only evaluate the performance qualitatively since the noise-free images are always absent in reality, i.e., we evaluate the restoration results by the visual effect. To obtain both the quantitative and qualitative results, we use the simulate dataset Washington DC Mall as the simulated noise-free image in this study as [11] does. For evaluation purpose, three kinds of common noise are added into this dataset. First, zero-mean Gaussian noise is added into all bands of HSI. Considering the intensity of noise is varied for different bands, we add different bands with different noise intensities. The SNR of the resulted band is ranging from 10 db and 20 db. Second, we added into HSI uniform noise. Third, we add dead lines, whose width varied from two to three lines, into the bands of 70 th to 73 rd. For fair comparison, before adding noise into the original HSI, we normalize the gray values of each band between (0, 1)first. Then, we add noise into the normalized image. Finally, the gray values of the denoised image are stretched to the level of original HSI. Figures 3 and 4 illustrate the experimental results on bands 2 and 100, where two areas of interest are zoomed for a detailed comparison. Those two bands are influenced by Gaussian noise as well as uniform noise. Original clean/noise-free band and the noisy band are shown in (a) and (b). The restoration results via VBM3D, Godec, SLrank, and low-rank methods are given in (c)-(f). By comparing the visual results, it can be seen that the proposed low-rank method has best restoration result among those four methods. The results of Godec based and SLrank based method are oversmoothed and some noise still exists in the denoised image by VBM3D method. This demonstrates that the proposed method functions well for the noisy image. For SLrank based method, its denoising performance is inferior to the proposed method. The reason is given as follows. SLrank based method pays attention on how to accurately recovery image from Gaussian noise or sparse noise polluted images, while the proposed method focuses on a totally new perspective (i.e., how to deal with more kinds of noise) of HSI denoising, which is seldom considered but different with the conditions that SLrank obeys. Figure 3: Visual comparison on band 2 of Washington dataset: (**a**) Clean/noise-free image band, (**b**) Noisy band, (**c**) Restoration result from VBM3D, (**d**) Restoration result from Godec, (**e**) Restoration result from SLrank, (**f**) Restoration result from the proposed method. Figures 5 and 6 illustrate the restoration results of incomplete bands 70 and 72, which is influenced by uniform noise, Gaussian noise, and dead pixels. The restoration results via VBM3D, Godec, SLrank, and low-rank method are given in (c)-(f). In these figures, two areas of interest are zoomed for a detailed comparison. From the visual results of different methods, it can be seen the results on those two noisy incomplete bands are similar to those in Figures 3 and 4. Noise still obviously exists in the results of VBM3D method. Though Godec based method has comparable restoration results with the proposed low-rank method, some band (band 70) is oversmoothed. Since low-rank matrix analysis is capable of handling the missing data, it can be seen that Godec based, SLrank based, and the proposed low-rank methods simultaneously fill the missing values as well as remove the noise. On the contrary, the dead lines still exist for VBM3D based methods. Figure 4: Visual comparison on band 100 of Washington dataset: (**a**) Clean/noise-free image band, (**b**) Noisy band, (**c**) Restoration result from VBM3D, (**d**) Restoration result from Godec, (**e**) Restoration result from SLrank, (**f**) Restoration result from the proposed method.