# Hyperspectral Image Inpainting Based on Robust Spectral Dictionary Learning
## 5 Experimental Results and Analysis
### Simulated Data Experiment  
The Pavia Centre HSI was used to construct simulated data ([[http://www.ehu.eus/ccwintco/index.php?Title=Hyperspectral_Remote_Sensing_Scenes](http://www.ehu.eus/ccwintco/index.php?Title=Hyperspectral_Remote_Sensing_Scenes)]([http://www.ehu.eus/ccwintco/index.php?Title=Hyperspectral_Remote_Sensing_Scenes](http://www.ehu.eus/ccwintco/index.php?Title=Hyperspectral_Remote_Sensing_Scenes))). The Pavia Centre scene was acquired by the reflective optics system imaging spectrometer (ROSIS) sensor during a flight over Pavia, northern Italy, with atmospheric correction [34]. Each pixel in the scene includes 102 spectral bands between 0.43 \(\upmu\)m and 0.86 \(\upmu\)m. For the convenience of analysis, the chosen spatial size of the data was 201 \(\times\) 201 pixels here, as shown in Figure 1. To simulate the clean image, high level noise bands were removed and totally 80 spectral bands were remained. This data set was considered to be a clean image in this section, and each band of data was normalized before adding noise and missing strips. The effects of four types of noise were considered in the experiment: Gaussian independent and identically distributed (i.i.d) noise, Gaussian non-i.i.d noise, Laplacian noise, and Poisson noise. The Gaussian i.i.d noise was taken to have a zero mean and a variance of \(\sigma=0.10\). The Gaussian non-i.i.d noise obeyed the distribution \(\mathbf{n}_{i}\sim\mathbf{N}\big{(}\mathbf{0},\mathbf{D}_{d}^{2}\big{)}\), where \(\mathbf{D}_{d}\) is a diagonal matrix with the diagonal elements uniformly distributed in the (0, 1) range. The Laplacian noise scale was set to 30. The Poisson noise obeyed the distribution \(\mathbf{Y}\sim P(\varphi\mathbf{X})\), where \(P(\mathbf{W})\) represents an independent Poisson random variable matrix of size \(\mathbf{W}\), and the parameter is given by the corresponding elements \(\mathbf{W}:=\big{[}w_{ij}\big{]}\). The signal-to-noise ratio, \(\text{SNR}:\varphi\Big{(}\sum_{i,j}w_{ij}^{2}\Big{)}/\big{(}\sum_{i,j}w_{ij} \big{)}\), was set to 15 dB using parameter \(\varphi\). The setting of the missing strip was done following a previous report [12], and the position of the missing strip was known. In dictionary learning process, the regularization parameter \(\lambda\) of the proposed INORSDL is set to 1. To quantitatively assess the effectiveness of the algorithm, the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) indicators were used to quantitatively evaluate and compare the image inpainting performance of each algorithm. The PSNR was used to measure the degree of similarity between the inpainted HSI as a whole and the original real image. SSIM is a quantitative evaluation method based on human vision. It can better reflect the quality of visual perception of an image and gives emphasis to the structural information of the images, making it suitable for the spatial dimensions of HSIs. Figures 2-5 show the results of various hyperspectral inpainting algorithms for Gaussian i.i.d noise, Gaussian non-i.i.d noise, Laplacian noise, and Poisson noise, respectively. For Poisson noise, the algorithm proposed herein first transformed the Poisson noise into an approximate additive Gaussian noise with an approximately equal variance using the variance stability transformation [35] and subsequently processed it. The inpainting results of different algorithms under various noise conditions show that all the inpainting algorithms could restore the missing strips in the image, but the LLRSSTV algorithm could not completely restore the missing strips, which is evident in Figure 2. Because the PDE algorithm only inpaints missing pixels and does not perform simultaneous denoising on the image, there was still noise in the output image after the algorithm was applied. In sharp contrast, the UBD, LLRSSTV, BPFA, and INORSDL algorithms removed a large portion of the noise while restoring the missing pixels.