I've created Drupal module "RESTful web services support for files and images", which I believe is exactly what you were asking for:

Hope it helps.

Disclosure: I'm the maintainer of this module, I hope this does not violate the site's policy on self-promotion.

I created (and I am maintaining) the RESTful web services support for files and images module, which I believe does exactly what you were asking for.

This module provides support for creating and updating fields of type file and image. It accepts (multiple) image/file data as base64_encoded strings in the JSON payload.

It requires the RESTful Web Services module.