Image Translation by Ad CycleGAN for COVID-19 X-Ray Images: A New Approach for Controllable GAN

. 2022 Dec 8;22(24):9628. doi: 10.3390/s22249628

Algorithm 1. Ad CycleGAN Optimization
1:	for number of epochs do
2:	for number of batches do
3:	Sample minibatch $\leftarrow {\{x^{(i)}\}}_{i = 1}^{m} \in X$
4:	Sample minibatch $\leftarrow {\{y^{(j)}\}}_{j = 1}^{m} \in Y$
5:	Generate m synthetic samples of $G (x) a n d F (y)$
6:	$s y n t h e t i c X : X \to G (x)$
7:	$s y n t h e t i c Y : Y \to F (y)$
8:	Compute the Adversarial loss
9:	$L_{G A N} (G, D_{Y}, X, Y) = E_{y ~ p (y^{(m)})} [\log D_{Y} (y)] + E_{x ~ p (x^{(m)})} [\log (1 - D_{Y} (G (x)))]$
10:	$L_{G A N} (F, D_{X}, Y, X) = E_{x ~ p_{d a t a} (x)} [\log D_{X} (x)] + E_{y ~ p_{d a t a} (y)} [\log (1 - D_{X} (F (y)))]$
11:	Generate m cycle sample of $F (G (x)) a n d G (F (y))$
12:	$C y c l e X : G (x) \to F (G (x))$
13:	$C y c l e Y : F (y) \to G (F (y))$
14:	Compute the Cycle loss
15:	$L_{c y c} (G, F) = E_{x ~ p (x^{(m)})} [F (G (x)) - x_{1}] + E_{y ~ p (y^{(m)})} [G (F (y)) - y_{1}]$
16:	Generate m identical sample of $F (x) a n d G (y)$
17:	$i d e n t i c a l X : X \to F (x)$
18:	$i d e n t i c a l Y : Y \to G (y)$
19:	Compute the identity loss
20:	$L_{i d e n} (G, F) = E_{x ~ p (x^{(m)})} [F (x) - x_{1}] + E_{y ~ p (y^{(m)})} [G (y) - y_{1}]$
21:	Compute the criterion loss for cycle sample: $L_{c - c y c l e}$
22:	Compute the criterion loss for identical sample: $L_{c - i d e n t i t y}$
23:	Compute the total generator loss
24:	$L_{t o t a l} = [L_{G A N} (G, D_{Y}, X, Y) + L_{G A N} (F, D_{X}, Y, X)] + λ L_{c y c l e} (G, F) + λ L_{i d e n} (G, F) + κ (φ L_{c})$
25	Update the Discriminator $D_{X} a n d D_{Y}$
26:	$m a x_{D_{X}} L_{G A N} (F, D_{X}, X, Y)$
27:	$m a x_{D_{Y}} L_{G A N} (G, D_{y}, X, Y)$
28:	Update the Generators $G, F$
29:	$m i n_{G, F} L (G, F, D_{X}, D_{Y})$
30:	end do
31:	end do