# End-to-End Classification Network for Ice Sheet Subsurface Targets in Radar Imagery
## 2 Materials and Methods
### Noise Removal during Image Pre-Processing  
Ground-penetrating radar is capable of retrieving sample data across vast areas of ice, but the resulting images are often plagued by speckles and other types of interference. Speckle noise reduces the quality of radar images, and seriously hinders the interpretation and further interpretation of images (i.e., image feature extraction, image segmentation, etc.). Radar image quality can be improved with a number of noise-reduction techniques. [PERSON] et al. [4] successfully denoised images using the anisotropic diffusion method, which requires regional filter smoothing. [PERSON] et al. [3] applied an undecimated wavelet transform to decompose the ice radar image into wavelet sub-bands, and then improved overall image quality using threshold processing. Radar image noise reduction must not only reduce noise, but also maintain relatively complete edge information. Inspired by the work proposed by [PERSON] and [PERSON] [22], in which a bilateral filtering method reduces speckle noise and maintains image edges, we employ bilateral filtering to reduce the noise in the radar images in our proposed classification framework.  
Figure 2: Our network architecture consists of ResNet module, improved atrous spatial pyramid pooling (ASPP) module and decoder module.  
Bilateral filtering [22] is a filtering method that considers both the spatial and range information of an image. The method is non-iterative, local, and simple. Bilateral filtering model can be described as  
\[h(x)=k^{-1}(x)\int\limits_{-\infty}^{+\infty}\int\limits_{-\infty}^{+\infty}f( \xi)c(\xi,x)s(f(\xi),f(x))d\xi \tag{1}\]  
with the normalization  
\[k(x)=\int\limits_{-\infty}^{+\infty}\int\limits_{-\infty}^{+\infty}c(\xi,x)s( f(\xi),f(x))d\xi \tag{2}\]  
where \(f(\cdot)\) and \(h(\cdot)\) are the input and output image, respectively. \(x\) denotes the current pixel, and \(\xi\) references the pixels adjacent to pixel \(x\). \(c(\xi,x)\) signifies the geometric distance between \(x\) and \(\xi\). \(s(f(\xi),f(x))\) approximates the grayscale value between \(x\) and \(\xi\). \(c(\xi,x)\) and \(s(f(\xi),f(x))\) are expressed as  
\[c(\xi,x)=\exp{(-\frac{1}{2}(\frac{\|\xi-x\|}{\sigma_{d}}))}^{2} \tag{3}\]  
\[s(f(\xi),f(x))=\exp{(-\frac{1}{2}(\frac{\|f(\xi)-f(x)\|}{\sigma_{r}}))}^{2} \tag{4}\]  
where \(\sigma_{d}\) denotes geometric distance variance and \(\sigma_{r}\) denotes approximate variance of the grayscale value.  
From (3), we can see that the points far from the center x in space have little influence on the final filtering result of x. Spatial filtering weights the adjacent points in space, and the weighting coefficient diminishes with the increased distance. From (4), we can see that the range filtering weights the adjacent points with similar grayscale values, and the weighting coefficient decreases with the large variation in adjacent pixel grayscale values. Because bilateral filtering includes both spatial and range information of the image, it can significantly reduce speckle noise in radar images. We use bilateral filtering [22] in training and test images, which allows for noise reduction of images and improves classification performance in the radar images.