I am trying to figure out slowly how the following artwork is produced. Would you guys have any clue? It looks like the base work is a photograph, but has a lot of similarities with these faded, vintage illustrator grain gradients as well. In sum, I have no clue and really want to figure this out
Apparently this artwork is called Rimova and was made by Nicholas Law. Most of his art seems to have the same look so I'm sure that he has spent a lot of time refining this technique. A similar result is probably more than a few clicks away.
Obviously I can't tell you exactly how this was made, but I'll try to give you some inspiration for further experimentation. The following isn't meant as an in-depth step-by-step tutorial, and the result doesn't exactly match your reference, but I hope you agree that it points in the right direction.
First of all use Photoshop for this, don't use Illustrator. Illustrator is a vector based application best suited for working with geometrical shapes and type. Photoshop is a pixel based application much better suited for this kind of work.
I convert the image to a Smart Object so I can work non-destructively:
I add some Filter > Blur > Surface Blur to get rid of some of the texture of the original image:
I add a little Filter > Blur > Gaussian Blur to get that retro "out of focus" look:
Then some Filter > Noise > Add Noise to get the grainy look:
And finally I add an Gradient Map adjustment layer to map the lights and shadows of the original to a psychedelic color gradient:
My result looks like this:
Please remember, that this is 5-10 minutes of work. I'm sure the artist spent a little more time.
Since you've added "Photo-editing" as the tag I'll attempt an answer, but you can forget Illustrator. It's no good for editing photos which are raster images.
It's pretty easy to create similar effects in Photoshop, or other similar raster image editors.
In Photoshop you could take a regular photo, turn it into a Smart Object, then apply an Iris Blur to it, and then use the Adobe Camera RAW filter to apply split toning (orange highlights, and purple shadows), an exposure adjustment, and to add grain.
Smart Objects are really useful for work like this as you can apply filters to them non-destructively. This means all these effects can be adjusted later to your taste, without affecting the original image.
Obviously the quality of the result will depend on the quality of the original photograph.