How I can I get WordPress to stop making link-image URLs relative?

I'm trying to add logos to the blog-roll widget, but WordPress makes the URLs of the images relative to the current blog.

For example, if the site is example/blogs, the images in the blog-roll widget at the main blog work correctly, but the ones at example/blogs/foobar are broken because instead of using something like /common/bloglogos/main.png (or even .png), it uses .png.

I've tried various combinations of URLs and formats, but it always makes the images' URLs relative to the current blog which is annoying because it would require uploading the images for all of the blogs to each of them instead of having them all in a central location which can be updated as necessary with just one change.

The URLs of the links themselves are fine, it's just the URLs of the images of the links that are the problem.

To be clear, I'm talking about images associated with WordPress links. In the case below, instead of the WP links using the image at /whatever/something.png, it will append the URL to the sub-blog, resulting in the invalid URL .png. In fact, if I put .jpg in the field, it will use ://somesite/path/pic.jpg.