These are artefacts of the original photo?
You can use Photoshop to get rid of such things. It can be painstaking, careful work though. It's a skill, not a simple process.
Are they in the original photo?
They look like they also could originate from the digitization process. So maybe you could get it scanned again?
First, this is really a Photoshop issue, not Illustrator.
Second, scan the image do not take a photo and take it out of the frame - what you are seeing is reflections and the quality is poor.
If capturing with a camera is the only option, take it out of the frame, lay it on a flat surface and photograph straight down. This should elminate the reflections.
If this is your only available image - you can add layers in Photoshop to adjust the hue/saturation and then mask out the purple areas. You can also use a levels layer mask to remove the screen/window reflection in the top right.
Like Monika, I think it looks like scanning artifacts, such as those made from slides/transparencies, and there are many, including the notable stripes (green to the left/in the middle (wall (along with blue), shirt, arm, wrapping, tablecloth), purple to the right (tee)); remember the blue smudge on the tongue.
How about the regular stripes, Kevin?