Useful metrics to compare network-output image to true image?
Widely adopted method to measure similarity between two images is structural similarity:


Wikipedia 
Useful links
Implementation


However, if you aim on training a network that should produce images of desired properties, I would consider GANs framework. In this case, the similarity between the generated and target image is defined by a special discriminator network.
Depending on what is your task, there are many GAN sub-types.