JPEG compression only retains magnitude information? How about phase information?

I guess phase information is not useful at all, so JPEG just ignore them...

But is there any application that phase information can be useful?

And if we want to get the phase information,

1) How to get at the encoder side along with DCT coefficients magnitude
information? and then it can be transmitted to the decoder side...

2) How to get at the decoder side by inferencing from DCT coefficient
magnitude information, if they are not obtained at the encoder side and
transmitted to the decoder side...

Thanks a lot,

-Walalla