## 3 Single-Image Destriping Method
### Adaptive Moment Matching Stripe Noise Removal Model  
Ideally, the traditional moment matching method defines the stripe removal model as a linear formula and adjusts the mean and standard deviation of the images formed by each sensor to a reference value, as shown in Equation (1):  
\[DN_{cal,i}=\left(DN_{mw,i}-B_{i}\right)/NG_{i}, \tag{1}\]  
\[NG_{i}=\delta_{i}/\delta_{r}(\delta_{r}=\frac{1}{N}\sum_{i=1}^{N}\delta_{i}), \tag{2}\]  
\[B_{i}=Mean_{i}-NG_{i}\times Mean. \tag{3}\]  
where \(DN_{cal,i}\) is the grayscale value of the corrected pixel, \(DN_{mw,i}\) is the grayscale value of the original pixel, \(B_{i}\) stands for the gain of sensor \(i\), and \(NG_{i}\) stands for the offset of sensor \(i\). In formula (2), \(\delta_{i}\) is the standard deviation of each image column \(i\), and \(\delta_{r}\) is the reference standard deviation (In general, \(\delta_{r}\) is equal to the standard deviation of the whole image). In formula (3), \(Mean_{i}\) is the mean of each image column \(i\), and \(Mean\) is the reference mean (In general, \(Mean\) is equal to the average value of the whole image). The traditional method of moment matching adjusts the mean and standard deviation of all columns to the mean and standard deviation of the reference column, resulting in the mean value of the image column being approximately a straight line after moment matching. This method cannot reflect the distribution of the mean of the real image column, resulting in a ladder effect and changing the actual spectral distribution of the image. Different from this method, the adaptive moment matching method in this paper does not use the mean and standard deviation of the whole image, but uses the mean and standard deviation in the moving window, which is equivalent to smoothing the original column mean curve of the image. In addition, it is considered that the same moving window width is not entirely applicable to different bands, different stripe characteristics and different coverage areas. Therefore, we need to set the adaptive moving window size according to the gray level of the image and the land cover type. First, we should set the maximum value \(W_{max}\), minimum value \(W_{min}\) and the fixed window size \(W\) of the moving window. In general, we set \(W_{min}\) to be equal to the maximum width of the stripe in the image, and then set \(W_{max}\) to be equal to a quarter of the image width, and set \(W\) to be equal to half of the sum of \(W_{max}\) and \(W_{min}\). However, considering the characteristics of a large difference in the grayscale of the OHS data, for example, the water of the latter 16 bands has a large difference in grayscale from other objects, then the gray value of the water is so small that the column mean variance corresponding to a large moving window is very small. In this case, the upper limit \(W_{max}\) of the moving window needs to be lowered. Therefore, before setting the maximum value \(W_{max}\) of the moving window, the image column mean should be calculated first, and the attribute of the region on the image should be judged according to the column mean value. According to the set threshold value \(\rho_{b}\) (\(b=1\), \(2\),..., \(B\), \(B\) stands for the number of bands) and the comparison with the column mean value, the attribute of the region is divided into two categories: A high-brightness region (_column mean value_\(<\rho_{b}\)) and a low-brightness region (_column mean value_\(>\rho_{b}\)). For the former, we use a larger \(W_{max}\). Otherwise, we use a smaller \(W_{max}\). On the basis of the (\(W_{min}\), \(W_{max}\), \(W\)) corresponding to the two types of data, we obtain the minimum variance \(D_{Wmax\_min}\) corresponding to each \(W_{max}\), the maximum variance \(D_{Wmin\_max}\) corresponding to the each \(W_{min}\), and the variance value (\(D_{W\_min}\), \(D_{W\_max}\)) corresponding to each \(W\) width. Therefore, the upper and lower limits (\(D_{min}\), \(D_{max}\)) of the variance corresponding to the two types of moving window ranges are:  
\[\left\{