Colorization loss function

I’m getting started with image colorization and I came across this famous paper, Colorful Image Colorization but I don’t quite understand the loss function of this paper as my math is not that good. I checked some implementations in Paperswithcode site but that didn’t help much too.
I’d be really grateful if anyone can clarify the paper or share some good resources to best understand this paper and other works on Image Colorization. Thanks in advance.