Algorithm 1 HRGAN training algorithm.

Model: D: discriminator. G: generator. Gd: generator down-sampling. E: pre-trained MobileNetV3-small. Parameter: θdisc: discriminator parameters. θgen: generator parameters. Input: x: data set. y: one-hot encoded label vector. z: random noises sampled from a normal distribution. w: one-hot encoded label vector converted from random integer sampled from a normal distribution. Require: α: the learning rate of the generator. m: discriminator batch size. n: the ratio of discriminator and generator backpropagation. cls: the number of classes. MSreal: the pre-calculated MobileNet score of real data set. HR: the ratio of high-resolution output images and real images. $1: \mathbf{Initialization} {\theta }_{disc},{\theta }_{gen} \leftarrow \mathrm{Xavier} \mathrm{uniform}$ $2: \mathbf{while} {\theta }_{gen} \mathrm{has} \mathrm{not} \mathrm{converged} \mathbf{do}$ $3: \mathbf{for} \mathrm{i}=0,\cdots ,n \mathbf{do}$ $4: \mathrm{Sample} {\left\{x^{\left(i\right)}\right\}}_{i=1}^m ~{ \mathrm{P}}_{\mathrm{r}} \mathrm{a} \mathrm{batch} \mathrm{of} \mathrm{images} \mathrm{from} \mathrm{the} \mathrm{real} \mathrm{data} \mathrm{set}.$ $5: \mathrm{Sample} {\left\{y^{\left(i\right)}\right\}}_{i=1}^m ~{ \mathrm{P}}_{\mathrm{r}} \mathrm{a} \mathrm{batch} \mathrm{of} \mathrm{one}\text{-}\mathrm{hot} \mathrm{label} \mathrm{vectors} \mathrm{from} \mathrm{the} \mathrm{real} \mathrm{data} \mathrm{set}.$ $6: \mathrm{Sample} {\left\{z^{\left(i\right)}\right\}}_{i=1}^m ~ p\left(z\right) \mathrm{a} \mathrm{batch} \mathrm{from} \mathrm{a} \mathrm{normal} \mathrm{distribution}.$ $7: gra{d}_{{\theta }_{disc}} \leftarrow {\nabla }_{{\theta }_{disc}}\left[\begin{array}{c}\frac{1}{m}{\displaystyle \sum }_{i=1}^m\min \left(0,-k+D\left(x^{\left(i\right)},y^{\left(i\right)}\right)\right)\\ +\frac{1}{m}{\displaystyle \sum }_{i=1}^m\min \left(0,-k-D\left(G_d\left(z^{\left(i\right)},y^{\left(i\right)} \right),y^{\left(i\right)}\right)\right)\end{array}\right]$ $8: {\theta }_{disc}\leftarrow {\theta }_{disc}+2\alpha ·$$Adam\left({\theta }_{disc},gra{d}_{{\theta }_{disc}}\right)$ $9: \mathbf{end} \mathbf{for}$ $10: \mathrm{Sample} {\left\{z^{\left(i\right)}\right\}}_{i=1}^{2m} ~ p\left(z\right) \mathrm{a} \mathrm{batch} \mathrm{from} \mathrm{a} \mathrm{normal} \mathrm{distribution}.$ $11: \mathrm{Sample} {\left\{w^{\left(i\right)}\right\}}_{i=1}^{2m} ~ \mathrm{U}\left(0, cls-1\right)\in z \mathrm{a} \mathrm{batch} \mathrm{of} \mathrm{one}\text{-}\mathrm{hot} \mathrm{label} \mathrm{vectors} \mathrm{from} \mathrm{a} \mathrm{uniform} \mathrm{distribution}.$ $12: P\left(c|z^{\left(i\right)},w^{\left(i\right)}\right)\leftarrow \mathrm{softmax}\left(E\left(G\left(z^{\left(i\right)},w^{\left(i\right)}\right)\right)\right)$ $13: P\left(c\right) \leftarrow \frac{1}{2m}{\displaystyle \sum }_{i=1}^{2m}P\left(c|z^{\left(i\right)},w^{\left(i\right)}\right)$ $14: M{S}_{fake} \leftarrow \exp \left(\frac{1}{2m}{\displaystyle \sum }_{i=1}^{2m}{\displaystyle \sum }_{c=1}^{cls}P\left(c|z^{\left(i\right)},w^{\left(i\right)}\right)\log \frac{P\left(c|z^{\left(i\right)},w^{\left(i\right)}\right)}{P\left(c\right)}\right)$ $15: gra{d}_{{\theta }_{gen}} \leftarrow {\nabla }_{{\theta }_{gen}}\left[\begin{array}{c}-\frac{1}{2m}{\displaystyle \sum }_{i=1}^{2m}D\left(G_d\left(z^{\left(i\right)},y^{\left(i\right)} \right),y^{\left(i\right)}\right)\\ +\max \left(0,\log \left(M{S}_{real} · \sqrt{HR}\right)-\log M{S}_{fake} \right)\end{array}\right]$ $16: {\theta }_{gen}\leftarrow {\theta }_{gen}-\alpha ·$$Adam\left({\theta }_{gen},gra{d}_{{\theta }_{gen}}\right)$ $17: \mathbf{end} \mathbf{while}$