VGG Loss

VGG Loss is a type of content loss introduced in the Perceptual Losses for Real-Time Style Transfer and Super-Resolution super-resolution and style transfer framework. It is an alternative to pixel-wise losses; VGG Loss attempts to be closer to perceptual similarity. The VGG loss is based on the ReLU activation layers of the pre-trained 19 layer VGG network. With $\phi\_{i,j}$ we indicate the feature map obtained by the $j$-th convolution (after activation) before the $i$-th maxpooling layer within the VGG19 network, which we consider given. We then define the VGG loss as the euclidean distance between the feature representations of a reconstructed image $G\_{\theta\_{G}}\left(I^{LR}\right)$ and the reference image $I^{HR}$:

$l\_{VGG/i.j} = \frac{1}{W\_{i,j}H\_{i,j}}\sum\_{x=1}^{W\_{i,j}}\sum\_{y=1}^{H\_{i,j}}\left(\phi\_{i,j}\left(I^{HR}\right)\_{x, y} - \phi\_{i,j}\left(G\_{\theta\_{G}}\left(I^{LR}\right)\right)\_{x, y}\right)^{2}$

Here $W\_{i,j}$ and $H\_{i,j}$ describe the dimensions of the respective feature maps within the VGG network.