# The Paradigm Shift in Hyperspectral Image Compression: A Neural Video Representation Methodology
## 3 Proposed Methods  
### The Necessity of a Paradigm Shift in Hyperspectral Image Compression  
As mentioned before, there are significant issues when compressing hyperspectral remote sensing images by using traditional deep learning methods. Below, we will attempt to theoretically analyze the reasons behind these problems to the best of our ability. Problem (1): the currently available open-source datasets for hyperspectral images are insufficient to support deep learning models in extracting generalized features;  
Problem (2): the excessively high number of spectral channels in hyperspectral images limits the performance of convolutional neural networks;  
Problem (3): the optimization objectives of traditional deep learning-based compression methods partially lose their effectiveness. We provide the classical compression pipeline of deep learning-based methods:  
\[\underset{\Theta_{1}+\Theta_{2}}{\text{argmin}}L=\lambda\big{|}\big{|}x- \mathcal{F}_{\Theta_{2}}(\mathcal{F}_{\Theta_{1}}(x))\big{|}\big{|}+\mathcal{R }\big{(}\mathcal{F}_{\Theta_{1}}(x)\big{)} \tag{1}\]  
We denote the reconstructed image by \(\hat{x}=\mathcal{F}_{\Theta_{2}}(\mathcal{F}_{\Theta_{1}}(x))\) and the latent feature by \(\hat{y}=\mathcal{F}_{\Theta_{1}}(x)\). Naturally, \(\Theta_{1}\) and \(\Theta_{2}\) denote the encoder parameters and decoder parameters, respectively. \(\lambda\) denotes the Lagrange coefficient controlling the compression ratio, and \(\mathcal{R}\) represents the function (typically the Shannon entropy equation) calculating the compression ratio whose input is the latent feature from the input images. For an enhanced representation capability (namely, dense in this scenario) of the feature space, the transformed features are further constrained with a multilayer Gaussian likelihood as follows:  
\[p(\hat{y})\,\sim\,\sum_{k=1}^{K}\omega^{(k)}\mathcal{N}\Big{(}\mu^{(k)}, \sigma^{2(k)}\Big{)} \tag{2}\]  
In some works, the side information \(\hat{z}=\mathcal{Q}(\hat{y})\) is inserted to indicate \(p(\hat{y})\) as \(p_{\hat{y}|\hat{z}}(\hat{y}\big{|}\hat{z})\). However, as this will not affect the analytical results, we will not implement it. Here, we assume that batch optimization can achieve similar effects to overall optimization. In fact, in the field of computer vision, the former is more feasible in most cases and tends to achieve better generalization. Further, considering an input dataset consisting of \(N\) images, \(\mathbf{x}=[x_{1},x_{2},\ldots,x_{N}]\), Formulation (1) can be further transformed into the following form:  
\[ \begin{split}&\underset{\Theta_{2}}{\text{min}}\big{|}\mathbf{x}- \mathcal{F}_{\Theta_{2}}(\mathbf{Y})\big{|}\big{|}\\ &\text{s.t.}\ \mathbf{Y}\in\underset{\Theta_{1}}{\text{min}} \mathcal{R}\big{(}\mathcal{F}_{\Theta_{1}}(\mathbf{x}),\lambda\big{)}\end{split}  \tag{3}\]  
Feature \(\mathbf{Y}\) plays a key role in this optimization objective. Both \(\mathcal{F}_{\Theta_{2}}(\cdot)\) and the feasible domain of \(\mathbf{Y}\) determine the compression performance. For Problem (1): \begin{table}
\begin{tabular}{p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline \hline
**Method** & **Advantages** & **Disadvantages** & **Applicability** & **Limitations** & **Performance Indicators** \\ \hline [PERSON] et al. (2022) [25] & Enhances structure and detail preservation with edge-guided features & Weak interspectral information extraction & General hyperspectral images & Limited correlation exploration between bands & Improved edge preservation \\ \hline [PERSON] et al. (2024) [26] & Captures interspectral dependencies effectively & Suboptimal spatial compression & Hyperspectral images with adjacent bands & Weak handling of single-band spatial redundancy & Enhanced spectral modeling \\ \hline [PERSON] et al. (2024) [27] & Utilizes 3D convolutions for better spectral retention & High computational resource needs & Resource-rich environments & Unsuitable for resource-constrained scenarios & Spectral retention \\ \hline \hline \end{tabular}
\end{table}