In the html view, images are displayed like this:
element.image.url points to a
As far as I know it's not possible to pass additional headers with asset requests (scripts, images, media, CSS files that the browser loads while rendering the page). That's all controlled by the browser. Only when making a XHR (AJAX) request can you modify headers.
I would suggest looking at your server side authentication and seeing if there's a solution there.