# Inf-OSRGAN: Optimized Blind Super-Resolution GAN for Infrared Images
## 3 Method
### Degradation Model  
#### 3.1.1 Prior Research  
Blind super-resolution (Blind SR) represents a complex ill-posed inverse problem, positing that high-resolution (HR) images suffer from various forms of degradation. Typically, classic degradation models [52; 53] are used to synthesize low-resolution inputs:  
\[\mathbf{x}=\mathcal{D}(\mathbf{y})=[(\mathbf{y}\otimes\mathbf{k})\downarrow_{r}+\mathbf{n}]_{\text {JPEG}} \tag{1}\]  
where \(\mathcal{D}\) represents the degradation process. In general, the high-resolution image \(\mathbf{y}\) is convolved with a blur kernel \(\mathbf{k}\), followed by a downsampling operation with a scale factor  
Figure 1: Multiple-scene image samples. Our dataset encompasses a diverse range of scenes, including seascapes, animal imagery, industrial environments, urban landscapes, natural landscapes, indoor settings, portraits, surveillance perspectives, and viewpoints featuring vehicles. \(r\) and the addition of noise \(n\). Finally, the process concludes with the application of a commonly used JPEG compression, resulting in a low-resolution image \(x\). Traditional degradation models, although simple and mathematically convenient, often fall short in representing the spectrum of degradation present in actual low-resolution (LR) images. LR images may be affected by degradation such as blurring, downsampling, and various levels of noise with different orders. Therefore, a random shuffle strategy [16] is proposed to address this issue. The degraded sequence \(\{\mathbf{B}_{iso},\mathbf{B}_{aniso},\mathbf{D}^{s},\mathbf{N}_{G},\mathbf{N}_ { JPEG},\mathbf{N}_{s}\}\) is shuffled randomly, where \(\mathbf{D}^{s}\) denotes performing a downsampling operation with scale factor \(s\) randomly selected from the set \(\{\mathbf{D}^{s}_{nearest},\mathbf{D}^{s}_{bilinear},\mathbf{D}^{s}_{bichichic},\mathbf{D}^{s}_{down-up}\}\). In particular, \(\mathbf{D}^{s}_{down-up}\) sequences of \(\mathbf{D}^{s/a}_{down-up}\) and \(\mathbf{D}^{s}_{up}\) can be inserted into other degradations. To obtain more realistic degradation, ref. [44] enhanced the classic degradation model by extending it to high-order degradation processes. Classical degradation models, which can be considered as first-order modeling, only contain a limited number of degradations. In real-world scenarios, the degradation is varied and often involves multiple steps. These complex degradation processes cannot be adequately captured by a classic degradation model. Instead, a more sophisticated high-order degradation model is needed, which incorporates \(n\) repetitive degradation processes. Each degradation process within the model is described using a classical degradation model, as demonstrated:  
\[\mathbf{x}=\mathcal{D}^{n}(\mathbf{y})=(\mathcal{D}_{n}\circ\cdots\circ\mathcal{D}_{2 }\circ\mathcal{D}_{1})(\mathbf{y}) \tag{2}\]  
High-order degradation uses the same procedure but with varying hyperparameters. The term \"higher-order\" in this context refers to the execution time of the operation. The key aspect is the repeated execution of the operation with different parameters. While a random shuffle strategy and high-order degradation model are effective in managing complex degradation scenarios by encompassing all basic degradation types, they often overlook important extreme cases prevalent in the real world. These extreme cases involve combinations of different subsets of basic degradation types. In order to tackle this issue, ref. [17] introduced a degradation model that utilizes a gate mechanism to select the basic degradation types that should be randomly incorporated into the degradation process:  
\[I^{LR}=\mathcal{D}_{g}(I^{HR})=(\sigma_{g}(\mathbf{D}_{1})\circ\sigma_{g}( \mathbf{D}_{2})\circ\cdots\circ\sigma_{g}(\mathbf{D}_{m}))(I^{HR}) \tag{3}\]  
where \(\mathcal{D}_{g}\) represents the gated degradation process, and \(\mathbf{D}_{i}\in\{\mathbf{D}_{k},\mathbf{D}_{n},\mathbf{D}_{j},\dots\},i\in \{1,\dots,m\}\) denotes the basic degradation type.