Algorithm 2. HR and LR Relationship Acquisition Process

Input: Training set $T=\left\{\left(P_{H1}^{\prime },p_{L1}\right),\left(P_{H2}^{\prime },p_{L2}\right),\cdots ,\left(P_{HN}^{\prime },p_{LN}\right)\right\}$, where $p_{L\mathrm{i}}\in R$ is the value of the LR pixel, $P_{Hi}^{\prime }\in R^{{(R+2)}^2\times 1}$ is the corresponding pixel values within the region block of the HR projection image, $i=1,2,\dots ,N$, and η is the learning rate. Output: The predicted value of the LR pixel ${\tilde{p}}_{Li}\in R$. (1) Randomly select the initial value W(0). (2) Select the sample $\left(P_{Hi}^{\prime },p_{Li}\right)$ from the training set. (3) Calculate the output of the perceptron and the mean squared error.                   ${\tilde{p}}_{L\mathrm{i}}=W{P}_{Hi}^{\prime }$                   $Error={\displaystyle \frac{1}{2}}‖p_{Li}-{\tilde{p}}_{Li}‖$ (4) Update the weight coefficients using the SGD method.                 $W\leftarrow W-\eta {\displaystyle \frac{\partial Error}{\partial W}}$ (5) Repeat steps (2) to (4) until the stopping criteria are met (such as reaching the maximum number of iterations or error convergence).