Halftone dots are not noise, and treating them as noise destroys the picture

Take a 1950s newspaper photograph, scan it, and run it through any general-purpose image cleaner. It will get worse. Sharpen it and you get moire - shimmering interference patterns that were never on the page. Denoise it and the picture dissolves into grey soup. This is not a failure of the tools. It is a category error about what is actually in the image.

The dots are the encoding, not dirt on top of it

Before digital printing, a continuous-tone photograph could not be printed directly - a press can only lay down ink or not lay it down, with nothing in between. So the photograph was passed through a halftone screen that converted tone into dots of varying size at a fixed frequency and angle. A dark region became large dots, a light region small ones, and from a normal reading distance the eye blends them back into tone.

What is on the paper, then, is not a picture with some dots on it. It is a picture encoded entirely as dots. Treating the dots as noise to be removed is like treating the letters of a word as smudges to be cleaned off the page - you are deleting the very thing that carries the meaning.

Why scanning makes it shimmer

Scanning re-samples that regular dot pattern at a different regular frequency - the scanner's own grid of sensors. When two regular patterns overlap at slightly different frequencies, they interfere, and the interference is a new, coarse pattern that neither original had. That is moire. Sharpening amplifies it, because sharpening amplifies exactly the kind of high-frequency edge the interference is made of. Denoising suppresses it, but only by suppressing the encoding along with it.

Measure the screen, then remove at that frequency

The correct operation is not to blur and hope. It is to measure the screen's line frequency and angle directly from the page - these vary by press, by era, and by colour channel - and then remove energy at exactly that frequency and its harmonics, and nowhere else. Image detail lives at other frequencies, so it survives the operation untouched. The dots come out; the photograph stays.

Practical notes for scanning halftone material

• Scan at 600 DPI or better. The screen has to be resolvable before it can be measured; scan too low and the dots alias into mush before you have even started.
• Expect a different screen angle per colour channel on colour presses - that is what produces the rosette pattern - and measure each channel separately rather than averaging them.
• Text on the same page is line art, not halftone. It is excluded from descreening and restored by the text path, so headlines and captions stay crisp while the photograph is descreened.
• Keep the original scan. Descreening is a measured, reversible decision, and the raw dotted scan is worth retaining in case a future process wants to measure the screen differently.

The difference this makes

Do this and a newspaper photograph that looked like grey mush comes back as a photograph - faces, tones, depth, the things the halftone was encoding all along. Do the general-purpose thing and you get a cleaner, softer version of the mush, which is to say you get the mush with its last bit of structure sanded off.

You cannot clean an encoding. You can only decode it, or destroy it. Most tools destroy it and call the result clean.