Noise in digital images or photos is complicated... there are different types of noise, and sometimes the camera itself just takes noisy pictures, period. We've got a higher end Kodak [yes, I consider any point & shoot that sold for over $200 when the average was ~$75 to be *Higher End*, relatively speaking] that cannot take a picture that doesn't look splotchy when you zoom in, though its photos look fine as long as you don't.
Editing noisy images is limited... noise effects the way filters & adjustments work, & it's also common for editing, FX, filters, & adjustments to alter or even remove that noise, so you wind up with areas that have been noticeably retouched, not necessarily because of a poor job, but because the noise in those places is different, perhaps appearing as a different sort of texture; it's like when you touch-up a spot on a wall, & even though you used paint from the same can that you used when you painted the entire wall a year ago, it simply doesn't match.
So photographers 1st try to minimize noise when they take the picture [they know what cameras are noisy at what ISO], often try to remove what noise is there, & may try to match noise [e.g. add or match (film) grain] after editing. There are different ways to go about noise removal. One common method is to blur everything, usually followed with a sharpening filter to try & get rid of the worst effects of the blurring. Another is to treat noise like spots & scratches, looking for colors within an adjustable radius that don't match their neighbors, then blending them in -- this is common in image editing software, & it's often kind of meh. OTOH when the noise is part of just the color or brightness data in an image, IOW when you still have accurate, non-noisy data saved in the image file, an image editor's built-in filtering might work pretty effectively.
If you Google on noise reduction, filtering etc. you'll likely get a Lot of hits with research, code, papers etc. on different, sometimes theoretical approaches to reducing the noise in an image. You're most likely to see that stuff in practice with paid software & P/Shop plug-ins, but you can check out G'MIC, probably as a GIMP plug-in [gmic.eu], or maybe look at what's available in or with RawTherapee [rawtherapee.com].
And there's this:
Summerized From Robert Mizerek -- "Poor Man’s noise reduction"
Open the same image on 2 layers, to one layer apply a Gaussian Blur of 10 [that's for P/Shop so may want to experiment], combine [flatten] the 2 layers using the Color blend mode.
And today on GOTD we have Helicon Filter. I hadn't heard of it, but apparently it started life as image noise reduction software, & started to grow from there. The rest of the app isn't bad by any means, but my personal opinion, as always purely FWIW, is I wouldn't bother with it if not for its noise reduction. It doesn't have layers, so scratch it off the list as an editor, & it's too large for me to bother with just for the stereo [3D] effect it can add. It's noise reduction may turn out to be well worth keeping, maybe even buying the app -- the only way to be really sure is to try it over time with all sorts of images, comparing how it does to what its competition can manage, or more precisely, how their noise removal algorithms compare.
If it's of any use, here's what I posted in the comments...
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Took a good look at this one, & will keep it to give it a good tryout, adding it to my editing workflow to see how it works over time, with what sorts of images etc. Googling, I saw that Helicon Filter's original claim to fame was its Noise Reduction filtering, which seems good & well worth a shot... it will not *cure* a photo taken with a camera that always takes noisy pictures, but it looks like it'll help with images taken at a higher ISO where noise starts to creep in, as a more refined filter that resists the tendency to blur everything.
That's not all Helicon Filter Stereo is good for, but aside from the Stereo part of it, why you'd want to add it to your toolkit if you already use something like P/Shop &/or PaintShop Pro &/or the GIMP etc.
The program itself isn't hard to figure out, though it may be laid out differently from what you're used to, & the online Help file isn't bad, with an option to view & save it as a PDF file. There are no layers or objects, nor will you find the levels & curves controls you use in P/Shop & PSP. There is an image browser on the left, which can get covered up by the column showing thumbnails of images in the selected folder. Below that is the History window -- not as flexible as those other 2 apps mentioned, but workable, it takes the place of the usual prominent Undo. And like the column on the right side of the program's window, the whole thing can be collapsed to get out of your way.
The zoom control that's usually up top is at the bottom of the window on the right. Next to it are the controls for displaying your image in 2 windows, similar to many editors with before & after views. And on the far right, the column changes to reflect the tool you're using, with collapsible sections of controls. The preferences settings let you choose what appears on the toolbar at the top.
I'm picky about software installations, & a program's impact on both Windows & other installed software [good or bad that's just me]. I'm not thrilled with the installation routine of Helicon Filter Stereo, but the app itself has little impact on anything, adding a bit over 200MB. I can't complain about Helicon's developer(s) -- they're just adding Microsoft C/C++ runtimes that the app uses -- but adding those amounts to 500+ new registry entries, along with a bunch of files/folders [in the C:\Windows folder] that I don't need. Besides the Microsoft stuff, today's GOTD adds folders to Program Files or Program Files (x86), ProgramData, Users\ [UserName]\ AppData\ Local\, & Users\ [UserName]\ My Pictures\ -- I just copied all of those but the one in My Pictures from a VM where I had installed the app.
You add the key for activation under the Help menu, which itself can be hidden if the program's window is sized too small. If you click the About menu item [under Help] it shows a hardware ID. That of course varies with different devices or Windows installs -- I'm not sure if it varies by user, and you might want to check that if you have more than one user account set up in Windows.
Thanks GOTD & Helicon -- this is software I'd never heard of, & likely wouldn't have heard of if it wasn't on GOTD.