How to make an invertible mapping between two variables whose dimensions are different ?

[Wangbk-dl]

Maybe this is a stupid question, but I have been puzzled for quite a long time. In the image super-resolution task, the input and output have different dimensions. How to build such an invertible mapping between them ?
Take an example:
If I have a low-resolution(LR) image x, and I have had an invertible function G. I can feed LR image x into G, and generate an HR image y. But can you ensure that we could obtain an output the same as x when we feed y into G_inverse?

y = G(x)
x' = G_inverse(y) =? x

I would appreciate it if you could offer some help.