Heres a method of removing noise (speckles and dithering) from a jpeg or bad scan that sometimes works better than blurring or the Filter:Noise:Despeckle function...

1) in the Layers control palette, select the noisy layer that you want to clean up.

2) choose the Layer:Duplicate Layer menu-item; a duplicate layer automatically appears above the original and becomes selected.

3) choose the Filter:Blur:Smart Blur menu-item. in the Smart Blur* dialog, set the controls like this...

• Radius: 3.0
• Threshhold: 25.0
• Quality: High
• Mode: Normal

...and then reduce the radius setting as far as you can while making sure that the sample image still looks very smooth and noiseless (you'll probably find a good setting between 0.75 and 1.75). the sample image is going to look too simplified, but don't worry about that right now. OK the dialog when you're through.

4) you should now have the noisy version of the image on one layer, and the smart-blurred version on the layer above it. make sure that both layers are visible, and that the smart-blurred layer is selected, then adjust the Opacity slider on the Layers control palette to fade it down. with a little experimentation, you'll probably find an opacity level (somewhere between 25% and 65%) at which the detail from the noisy image shows through the smart-blurred image, but the noise is masked out. if you find a setting that you want to keep, merge the two layers.

(*note) the Smart Blur function is good for filtering out unwanted noise and details, and dramatically reduces the number of colors used in the image (which can be a big advantage if you're going to convert the final image to gif or jpeg). - gonZo

NOTE: Jpeg or Jpg's are a 16 million color format so there is no need to reduce colors as above. Gif's on the other hand are only 256 colors. - Imaginos

One time, just for kicks, I added noise to a completed picture. Just noised up the whole pic. It gave all parts a uniform look and gave the impression that she was photographed that way and it's just a poor scanning job. :) - Vitamin "C"