How to get a good scan of a matte finish photo?

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I have some pictures from a recent trip that were taken with a disposable
35mm camera. Obviously the picture quality is not great, partly because
disposable cameras don't take great pictures, and partly because they were
X-ray scanned 19 times through airports sometimes in checked luggage,
sometimes as carry-on. About half the scans were before exposure, the other
half after. They were Kodak 800 ISO. I wasn't expecting great results from
a single-use film camera, but it wasn't a safe area to be showing off an
expensive digital camera. Some of the pictures had good composition and are
interesting.

The 4x6" prints are a bit dull and not that sharp, however I would like to
digitize a few of them and add them to the digital camera set just because
they form part of the memories of that trip.

Unfortunately I let someone talk me into getting the matte finish and not
the glossy finish. When scanning these on a flatbed scanner, I get little
coloured speckles in the image from the finish on the print. Scanning
higher or lower resolution doesn't really help. So far the best I have come
up with is to scan at very high resolution, adjust levels, run the image
through a noise reduction program and then resize down and sharpen just a
touch.

Is there a better way, or should I just get the important ones reprinted on
glossy from the negative and then scan that. Can a photofinishing store
digitize and invert a negative directly with better results?

Thankyou in advance for anyones suggestions on this.

[Mark C.]

Interesting. I've never had that problem with a matte finish.
Does your scanner software have a descreening option?
Not that it's relevant to a matte finish, but it might produce
the same or better results without all the post processing.

Another thing that might work is to get a thin piece of clear
glass or acrylic and put it between the photos and scanner
glass.

[Colin D.]

If you have a good digital camera with good macro capabilities, you
could try re-photographing the prints. The speckles come about because
of reflections from the scanner lamp, and using a camera lets you choose
a more suitable light to shoot in.