The noise removal feature inside Photoshop is a poor substitute, so it's always preferable to go back to the raw file and do it there. This article explains how to bring the newly-fixed file into your existing layered file, with minimum time wasted. This works for both Photoshop and Elements.
First, make sure you've saved the file as a PSD (or Tiff, if that's your preference). Here's the example edit I've created for this tutorial. The "Background" layer is the photo, of course. "Layer 1" is a duplicate of the Background layer which I've used to do some cloning and healing. Then above that are all the adjustment layers for my colour correction work.
Once I make sure my PSD file is safely saved, I re-open the raw file, and make the necessary adjustments to the noise sliders. While I'm doing this, I give myself a stern lecture about getting it right the first time, dammit!
Then I open the new version into Photoshop:
I press Ctrl A (or Cmd A for Mac) to select the whole photo:
Then I press Ctrl C to copy it. This can also be done via the Edit menu, of course.
I return to the PSD file, and I highlight the Background layer:
Then I press Ctrl V to paste the new version into the PSD:
IMPORTANT: If my PSD involved no pixel editing (cloning, healing, etc), then my job is done. I can Ctrl E to merge the new image down onto the old image if desired, and save the PSD again, and everything is dandy. My carelessness only cost me a few extra seconds.
BUT: If, as in this case, there was some pixel editing, I have to re-do it. Why? Because the edited pixels were the noisy ones, of course. So I have to delete the pixel editing layer:
Then duplicate the new image layer (or add a blank layer, if that's your preference), and do the cloning and healing etc all over again:
While I'm doing this, I'm giving myself an even sterner lecture about getting my raw editing right the first time, because now I'm wasting serious time. I find cloning tedious in any circumstance ... but to be doing it twice on the same photo? That irritates me like crazy. And I'm sure you don't enjoy it either.
I hope you never have to use this tutorial, but if you do, I hope the process goes as smoothly as possible for you.
Some notes about this article:
Note 1. None of this is a better solution that getting it right the first time. Take care with your raw edits, and don't proceed to Photoshop until you're damn sure it's correct.
Note 2. Obviously noise isn't the only thing you can get wrong in a raw edit. You might mess up the white balance, or contrast, or whatever. But those things are MUCH more serious, because they impact the adjustment layers in your PSD as well.
The reason I wrote about noise on this page is that noise is really the only thing that can be fixed this easily. If you go back to your raw file to make another sort of change, you'll need to carefully check every adjustment layer in your PSD, to make sure it's still doing what you want it to.
Please don't be casual about this. I can't stress it enough. Even a small change in the white balance, for example, can mean that an adjustment layer which wasn't causing red channel clipping before, now is causing it.
See Note 1.
Note 3. Plenty of people will bleat about opening your raw file as a smart object into Photoshop. In my opinion, this is a pile of bunkum, and I discussed it thoroughly in this thread.
See Note 1.
Note 4. If you did SO much pixel editing in Photoshop before you discovered your mistake, and you can't stomach the thought of doing it all over again, well, so be it. Do your noise removal as best you can in Photoshop, and vow it won't happen again.
See Note 1.