## 4 Hyperspectral Image Destriping Method
### The Comparison of Single-Band Destriping Methods Based on the Same Paradigm
#### 5.1.2 Objective Evaluation of Data Quality  
In the objective evaluation standard, the radiation quality improvement factor IF is defined as the change of the gray level of the two images alone the stripe direction before and after the removal of the stripes. The calculation formula is as follows:  
\[IF=10\lg\left[\frac{\sum\
olimits_{i}[m_{IR}(i)-m_{IR}(i-1)]^{2}}{\sum \
olimits_{i}[m_{IE}(i)-m_{IE}(i-1)]^{2}}\right]. \tag{29}\]  
where \(m_{IR}(i)\), \(m_{IE}(i)\) represent the average of the ith column before and after the removal of the stripes, respectively. The larger the value of IF, the stronger the destriping capability of the algorithm.  
Information entropy H is a reflection of the amount of image information and an important indicator for measuring the richness of the image information. The larger the information entropy of the single-band image, the richer the amount of information. The calculation formula of image information entropy \(H(x)\) is:  
\[H(x)=-\sum\limits_{i=0}^{bit}p(i)\lg[p(i)]. \tag{30}\]  
where \(bit\) is the maximum gray value of the color depth, and \(p(i)\) is the probability density of the gray value \(i\).  
ICV is defined as the ratio of the mean to the standard deviation on an approximately isotropic region.  
\[ICV=\frac{R_{m}}{R_{S}}. \tag{31}\]  
ICV was calculated by selecting two uniform regions, where \(R_{m}\) and \(R_{s}\) represent the mean and standard deviation of the selected image region. The larger the ICV, the better the stripe removal effect.  
MRD calculates the change of a no stripe region, and thus measures the ability to retain the original healthy information. The smaller the MRD, the stronger the ability to retain the original image information.  
\[MRD=\frac{1}{MN}\sum\limits_{i}^{M}\sum\limits_{j}^{N}\frac{\left|y(i,j)-x(i, j)\right|}{x(i,j)}. \tag{32}\]  
where \(y(i,j)\) and \(x(i,j)\) are the pixel values in the destriped and raw images. \(M,N\) are row and column numbers.  
NR is the noise reduction ratio achieved by the destriped method and ID is the degree of image distortion [11]. We assume:  
\[\begin{array}{l}N=\sum\limits_{i=0}^{k}meanP(u_{i}),\\ S=\sum\limits_{j\
eq i}^{N-1}meanP(u_{j})\end{array} \tag{33}\]  
where \(u_{i}\) is the frequency component produced by stripes, and \(u_{j}\) is the frequency component caused by the raw image without stripes. \(N\) stands for the total power of stripes noise in the mean power spectrum, and \(S\) stands for the total power of clear image in the mean power spectrum.  
\[\begin{array}{l}NR=\frac{N_{0}}{N_{1}},\\ ID=\frac{S_{1}}{S_{0}}\end{array} \tag{34}\]  
where \(N_{0}\) and \(N_{1}\) stand for the value of \(N\) in original image and destriped image, and \(S_{0}\) and \(S_{1}\) stand for the value of \(S\) in an original image and a destriped image.  
Ideally, NR-\(>+\infty\) and ID -\(>\)1.  
Due to the poor effect of moment matching and MMUTV, the objective evaluation index is not calculated. Table 2 is the objective evaluation of results.  
Based upon the subjective quantitative evaluation criteria, compared with other algorithms based on the same paradigm, our algorithm can achieve the best balance of information retention and stripe removal.