## 2 The Proposed Method
### Reference Dark Background Correction  
The reference dark background image refers to the instrument's response output value when there is no light input. This value allows the spatial dimensional push sweep hyperspectral imaging system's instrument fixed-mode noise component (\(\varepsilon_{1}\)) to be calculated and separated. Denoising is then accomplished by removing the fringe component from the noisy image. Instrument fixed-mode noise is caused by the imaging principle of the spatial dimensional push sweep hyperspectral imaging system, and has a certain regularity. It must be removed before calculating the reflectance of tumor hyperspectral images; otherwise, it will not only affect the subjective visual effect of images, but also lead to deviations in the reflectance of biological tissues, affecting the subsequent diagnosis and classification work. In this paper, the law of the fixed-mode noise of the instrument is found through a lot of experiments and calculations, and the fixed-mode noise of the instrument is eliminated according to this law.  
The sample image is captured simultaneously with the reference dark background image, which is consistent with the hyperspectral image in both the spatial and spectral dimensions. Since the varied acquisition environment will also affect the detector's non-uniformity error, both the sample picture and the dark background image must be acquired simultaneously. Separating the edge and fringe noise of the reference image as much as possible is essential for removing non-uniform fringe noise based on the reference. Many papers have been published on the removal technology of edge extraction [14,33]. These methods usually adopt a threshold to distinguish between edge and fringe noise in the image to avoid edge blurring. However, this method incorrectly removes the weak edges of the image and preserves the strong fringe noise. WLS [34] is a good edge-preserving picture filtering and denoising technique. We smooth the reference dark background picture using the WLS algorithm, then subtract it from the original dark background image to obtain the reference dark background image's edge component in order to more effectively separate the edges of the reference dark background image. The algorithm for removing instrument fixed-mode noise (\(N_{1}\)) is shown in Formula (8):  
\[A^{\prime}(i,j)=A(i,j)-\omega[a(i,j)]*a(i,j)/dark\_m \tag{8}\]  
where \(A^{\prime}(i,j)\) is the new image after denoising, \(A(i,j)\) is the image after BLF-WLS smoothing, \(a(i,j)\) is the reference dark background image acquired synchronously, \(\omega[a(i,j)]\) is called the weighting coefficient, and the specific calculation is shown in Formula (9). \(dark\_m\) is the mean value of dark background data \(a(i,j)\) calculated by the band.  
\[\omega[a(i,j)]=\sum_{i=1}^{B}\sum_{s=1}^{M\times N}(f[a(i,j)]-a(i,j))\;/\;(M \times N\times B) \tag{9}\]Among them, \(f[a(i,j)]\) refers to the weighted least square filtering of the reference dark background image. The purpose of this step is to retain the edge value of the reference image to the greatest extent, and then subtract the value of the dark background image to obtain the edge value of the reference dark background image, and then average the value of the space and spectral dimension respectively, and, finally, obtain the weighted coefficient \(\omega[a(i,j)]\).