Image quality issues can be one of the more difficult problems to fix. There are a few ways to correct this issue:
High quality version
Replace the image with a higher quality version. This may mean sourcing the original image file, contacting the photographer, or downloading the full resolution from a stock photography website. For logos and illustrations – this may mean replacing the graphic with a vector version.
Reducing the size of the image
If the issue is low resolution, reducing the size/area of the image in the design may fix the issue (for example, if your image is 150PPI at 3” x 3” - when printed at 1.5” x 1.5” it will be 300 PPI).
See: What size can I print my image?
Upscaling
This is not a complete fix – however it may be the only way to resolve the issue for certain images if the above solutions are not possible. The image may print blurry or unclear (as per the up-scaled image able), however it might be the only solution possible in some cases.
Filters and Effects
Applying image filters to an image can reduce or hide the appearance of quality issues. Photoshop has a vast array of filters and effects you can apply to an image.
Converting to vector (Live Trace)
Blurring the image
Applying artistic filters or overlays
You may want to upscale the image before applying the filters.
Replacing the image
Sometimes the only solution is to find an alternative image that is high enough quality for printing.