# Multi-Range Sequential Learning Based Dark Image Enhancement with Color Upgradation
## 3 Methodology  
### Proposed Architecture MSR-MIRNeT  
Before training the proposed MSR-MIRNeT hybrid model, the MSR [4] and MIRNeT [5] models are trained and obtained output images based on our ground-truth image, as shown in Figure 2. The schematic architecture of our proposed hybrid MSR-MIRNet model is represented in Figure 3.  
Figure 2: Visual comparison of low-light enhancement approaches, ELD [20], ExDark [15], CID [21], Our proposed model output.  
From a given image \(X\), the network extracts low-level features \(X_{0}\) by applying a CONV layer. Subsequently, multiple numbers of blocks of recursive residual groups (RRGs) permit feature maps \(X_{0}\) to pass over the RRG with surrounding deep features \(X_{d}\). We merged difference-of-convolution with rectified linear activation function-ReLU for an analogous role with difference-of-Gaussian and the color restoration function, which is compiled with the mapped function. The significant difference between the MSR [4], the MIRNeT [5] model, and our model is that our maximum parameters are designed to learn from the training data to enhance the images. In contrast, in MSR some parameters, such as variance and others, constantly depend on artificial settings. Here the multi-Scale residual is merged with RRG, then CONV \(1\times 1\) is applied for image color restoration, which generates \(I\in\mathbf{R}^{(l\times w\times 3)}\) and \(3\times 3\) layers for enhancement as precise features \(X_{d}\) and derives the remaining image \(R\in\mathbf{R}^{(l\times w\times 3)}\). After the color restoration process, some features may have an average value, which reduces the brightness of the generated image. Thus, a \(3\times 3\) CONV layer is used after color restoration to maintain the output RGB image standard. Hence, using the logarithmic transformation \(Tf(I\in\mathbf{R}^{(l\times w\times 3)})\), a low-light image is mapped with a bright image to enhance the output image. This can be represented using Equation (3).  
\[G(I\in\mathbf{R}^{(l\times w\times 3)})=Tf(I\in\mathbf{R}^{(l\times w\times 3 )}) \tag{3}\]  
Here, \(I(\in\mathbf{R}^{(l\times w\times 3)})\) is the input image after color restoration and \(T\) is the transformation function. \(Y_{0}=G(I\in\mathbf{R}^{(l\times w\times 3)})\) is the final enhanced image. Finally, the equation of repaired image is as follows:  
\[Y=I_{0}+R+Y_{0} \tag{4}\]  
In this experiment, the Charbonnier loss function [5] is used to optimize the pixel loss, which is defined as in Equation (5).  
\[L(Y_{0},X^{*})=\sqrt{(||Y_{0}---X^{*}||^{2}+\varepsilon^{2})} \tag{5}\]  
Here, \(X^{*}\) is the ground truth image and \(\varepsilon\) represents the constant with a value of \(10^{-4}\) in all experiments. Consecutively, with the combination of multi-range logarithmic transformation \(f_{1}\), difference-of-convolution \(f2\), color upgradation \(f_{3}\), and output image enhancement \(f_{4}\). Our model can be defined as in Equation (6).  
\[f(X)=f_{4}(f_{3}(f_{2}(f_{1}(X)))) \tag{6}\]  
Figure 3: MSR-MIRNeT Model Architecture.  
\(F(x,y)=Ke^{-((x^{2}+y^{2}))}/2\sigma^{2}\) is the neighboring Gaussian function, Here, \(K\) is constant and \(\sigma\) is the Standard Deviation of the Gaussian Function.