Sometimes artwork can have two different halftone patterns and one pass of descreen wont completely get rid of them.
Here is the original image.
And after descreen the blue letters still aren't descreened enough.
Different areas can be descreened separately using layers. Then you can delete the areas where different descreen is needed so that other layers can show through.
Start by duplicating the original layer. For the top layer. Select a descreen that matches most of the page.
Then turn off visibility of the top layer so that it's no longer seen. Select the bottom layer so it is now the active layer
Select a descreen value that works well. You might have to turn off automatic mode and manually adjust it for the smaller area.
Once the layer has been descreened. Use the magic wand (make sure to set it to ADD mode). Select the areas that needed special descreening.
Next go to Select and open Grow/Shrink. Use a positive number to increase the perimeter of the selection. This image was scanned at 800DPI, and 2 pixels works well.
Now click back on the top layer to make it the active layer.
Use the eraser or other means to erase/delete the selected area. This will cute a "hole" in the top layer so that you see the layer below it which has the different descreen algorithm.
Here is a comparision of 1 descreen pass vs 2 passes
Descreening Two Different Patterns
Re: Descreening Two Different Patterns
For a follow up, here is how to fill in the large blue area with a solid color to get rid of the pattern
Link: viewtopic.php?p=14#p14
Link: viewtopic.php?p=14#p14