# A Multichannel-Based Deep Learning Framework for Ocean SAR Scene Classification
## 3 MCNN Framework for Geophysical Phenomenon Classification
### Data Augmentation
To further squeeze the edges of SAR images when stretching other areas, we use the following image warp \(M_{\text{S},I}(x,y)\) to optimize the image quality:  
\[\underset{u(x,y)}{\underset{(}}\int\limits_{\text{$[0,1]^{2}$}}[u_{x}^{2}+u_{ y}^{2}+\mu(u(x,y)-m(x,y))^{2}]*\phi(x,y)dxdy. \tag{15}\]  
For the \(x\)-component, we replace \(m(x,y)\) with \(mx\) and set \(\phi(x,y)=1+\lambda E_{x}(x,y)\). For the \(y\)-component, we have \(m(x,y)=my\) and \(\phi(x,y)=1+\lambda E_{y}(x,y)\). \(E_{x}(x,y)\) and \(E_{y}(x,y)\) are the implementation of the x- and y-components, respectively, in the Canny edge detector [59]. To adjust the sample distribution of all classes, we apply the oversampling technique. Additionally, oversampling approaches generate synthetic instances to further benefit this task, whose typical techniques include image mixing, feature augmentations, and deep learning-based methods like generative adversarial networks (GANs) [63]. For the sake of diversity, we choose GANs as our data oversampling method. This story for data augmentation follows a typical neural network development process of data preparation, training, and generating new samples. To perform oversampling on a SAR dataset, an initial step involves training a generative adversarial network (GAN) to estimate the underlying distribution of oceanic data. Subsequently, the trained generator component of the GAN is employed to generate supplementary samples specifically focused on augmenting the representation of the minority class. In this design, we use a GAN to achieve the conditional distribution \(Py|x\). The GAN facilitates the training process by enabling robust discriminators (D) that yield informative gradients to the generator, even in scenarios where the quality of the generated samples is suboptimal. This characteristic enhances the training stability, contributing to more effective and reliable model convergence. To further optimize the GAN's loss function for categorical variables on GAN-based oversampling, we adopt the Wasserstein-1 distance (WD) by modifying the GAN objective to the following equation:  
\[\underset{G}{min}\underset{D}{max}\ \mathbb{E}_{x\sim p_{data}}[D(x)]-\mathbb{E}_{y \sim p_{y}}[D(G(y))]-\lambda\mathbb{E}_{\mathcal{A}\sim p_{x}}[(\parallel \
abla_{\hat{x}}D(\hat{x})\parallel_{2}-1)^{2}]. \tag{16}\]  
In this model, the generator \(G\) produces synthetic data samples that are indiscernible from authentic data and the discriminator \(D\) differentiates authentic instances from the training dataset and synthetic instances generated by the generative model \(G\). The variable \(\lambda\) is the penalty coefficient. \(D\) is a k-Lipschitz function, and this Lipschitz continuity condition is ensured through the process of clipping [64], where the weights of \(D\) are constrained to a bounded interval [\(-\)c, c]. The gradients are computed based on linear interpolations \(\hat{x}\sim p_{\hat{x}}\) between actual and synthetic samples, where \(p_{\hat{x}}\) represents the probability distribution of these linear interpolations.