Removing noise and descreening images in Photoshop
Noisy scans are a real pain - this is caused by a number of factors like digital camera images, low level light situations and scanning in halftone images. It is tricky to get rid of the noise but keep image definition and sharpness at a reasonable level - simply blurring the whole image will not do the job at all for any budding Photoshop Ninja! There is a number of ways to get rid of this, which I will outline below.
METHOD 1 - BETTER FOR ALL OVER NOISE AND HALFTONE PATTERN DECREENING
First convert your image to LAB colour. This turns your image into a 3 channel image, but different in composition to any other multi-channel image, check out the channels in your channels palette - they look quite different! Basically it breaks it down to the L channel which holds all the image contrast and detail, and the A and B channels that hold all the colour information.
You should hopefully discover that the A and B channels are most noisy. Filter these channels with with a light Gausian Blur, ensuring you use the same settings on each. You can actually get away with quite heavily filtering these channels as remember that all the image detail is held in the L channel.
Once these are smoothed out, go to your L channel and apply either the despeckle or median filter - the aim here is to remove as much noise as possible whilst still keeping the definition and sharpness of the edge detail. If it is really bad you may try the dust and scratches filter on selective areas - this filter shouldnt really be used over a whole image (or channel in this case). To use this in particularly bad areas simply apply the filter at the lowest settings that get rid of your noise, undo this and use your history brush. Once you have got rid of most of the noise or screen patterning you probably will want to sharpen up the L channel a little with the Unsharp Mask filter to improve definition.
Once you have finished, always remember to convert your image back to your desired working colour depth - probably either CMYK (for print) or RGB (for on-screen and web).
METHOD 2 - BETTER FOR ISOLATED AREAS OF NOISE IN SHADOW
The colour replacement tool is really good for getting rid of isolated noisy areas, often seen in the shadows and flat areas of midtones in digital camera shots. Simply brush over the affected areas with the tool and this should get rid of that nasty multi-coloured noise!
Bonus Tip
The first technique is also great for getting rid of the blocky artefacts that can appear in over compressed JPEGs. Digital camera shots are particularly vulnerable to picking up noise in the blue channel in their native RGB colour depth, if you are in a rush and need a quick fix you can often just apply a light despeckle or median filter to just this channel to remove a lot of noise.
Bonus Tip 2
If you find yourself having to scan in material from a commercially printed source you will almost definitely pick up the half-tone screen pattern of the print. If you really want to get the most out of the image, scan it in at the very highest optical resolution of your scanner. Work through the steps in method 1, but before you get to the final sharpening stage, resize your image down in 50-75% increments - this can help by averaging the resampled pixels.