Randy H. answered • 06/25/19
Certified Adobe Education Trainer with 30 Years Teaching Illustrator
The short answer is that you're never going to improve the quality of an image in Adobe Illustrator. It needs to be a high-quality image before you bring it into Illustrator.
That means you need to bring clean, clear and quality high-resolution pixel images into Adobe Illustrator to export quality pixel images out of it. Illustrator cannot fix that. If you're asking for good rules, bring your images into the program with an effective resolution of at least 200dpi at the display size (height and width in inches/cm, resolution-independent) you see at 100% zoom in Illustrator without fine lines/detail that will disappear when you reduce the resolution for (what I assume are) web-quality graphics you want to export.
Your screen lies to you because the resolution you see onscreen (72ppi on Macs at 100% display view percentage; as much as 96ppi on Windows-based systems) generally isn't true compared to your scaled end product you create. In this case, what you see isn't what you're eventually going to get. Your screen is lying to you. You need to improve pixel-based images in a pixel-manipulation product like Adobe Photoshop before you bring them into Illustrator. Then export the end product at lower resolution from Illustrator to create your web-quality graphics.
You're kinda handicapped by using an older version of Adobe Illustrator/Photoshop like Creative Suite 3. But even if you use the latest version of Adobe Photoshop to process your images and Illustrator to output your end product, there isn't much you can do to improve the quality of poor pixel graphics you bring into the process.
No offense intended, but without high-quality and high-resolution pixel graphics, there's no way to prevent the end result of Garbage In/Garbage Out.
