Some time ago poqudrof did some amazing work with extending the support for svg.
#4168

One of the things he worked on was support for base64 images.
Unfortunately this is only for SVG.

To quote him on another aspect:

Here are the bad parts : 

• I introduce some code duplication in :

private void loadBase64Image() 

Basically his loadBase64Image was some kind of copy of the loadImage of processing.
There where some down sites with that:

• Error messages are inconsistent (no cmyk error anymore etc.)
• Error assumed the extension format was 3 chars, so on tiff or jpeg it would report tif and jpe.
• Due to code duplication it is harder to maintain
• certain image formats like tga and tiff are no longer supported
• It assumes that data:image/ is always base64, but this is not always the case

I cleaned things up so the loadImage for the SVG is the loadImage from PApplet now.
And I added support for all the types he did not support with loadImage.

In other words, there is full base64 support now for loadImage.

Here is a gist to check it:

https://gist.github.com/clankill3r/03f4a7dbc64a4b48fbace1912b99c678