How can I get a large file-size background image to display when printing, saving or exporting figures?

I am plotting data over a background image like so:

It looks great on my screen, But, whether I use the built in functions "save" or "print" or custom functions like "export_fig", the exported image loses the background image:

The filesize of the background image is ~17 MB. If I vastly reduce the size, it exports with the background image, but resolution suffers. Is there a function I can use that will keep the original resolution, even though the filesize will be large?