Table 1 Common loss functions in...

Table 1

Common loss functions in surveyed papers.

Loss	Function example	Citation
L₁	$\sum_{i = 1}^{n} \| y_{t r u e} - y_{p r e d i c t e d} \|$	Widely adopted
L₂	${\sum_{i = 1}^{n} (y_{t r u e} - y_{p r e d i c t e d})}^{2}$	Widely adopted
Perceptual	$L_{p} (y, \hat{y}) = \sum_{v = 1}^{N} {‖ Φ^{v} (y) - Φ^{v} (\hat{y}) ‖}_{2}$	[50]
VGG	$\frac{1}{W_{i, j} H_{i, j}} \sum_{x = 1}^{W_{i, j}} \sum_{y = 1}^{H_{i, j}} (ϕ_{i, j} {(I^{H R})}_{x, y} - {ϕ_{i, j} {(G_{θ_{G}} (I^{L R}))}_{x, y})}^{2}$	[33]
Adversarial	$\frac{1}{2} E_{z} [l (D (z, y) - 1)] + \frac{1}{2} E_{z} [l (D (z, \hat{y}))] + \frac{1}{2} E_{z} [l (D (G (z) - 1))], where l (x) = x^{2}$	[50]
LSGAN (D)	$\underset{D}{m i n} V_{L S G A N} (D) = \frac{1}{2} E_{x ~ p_{d a t a} (x)} [(D (x) - b)^{2}] + \frac{1}{2} E_{z ~ p_{z} (z)} [{(D (G (z)) - a)}^{2}]$	[45]
LSGAN (G)	$\underset{G}{m i n} V_{L S G A N} (G) = \frac{1}{2} E_{z ~ p_{z} (z)} [(D (G (z)) - c)^{2}]$	[45]

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