Difference Between Empty Attribute And Undefined Attribute

I'll trying to tell the difference between the following three cases:

<img alt="text string" />
<img alt="" />
<img />

I can do this in Firefox with the following code, where elem is the
HTMLElement representing each image, but IE doesn't seem to
differentiate between empty string and undefined.

var alt = elem.getAttribute('alt');
alt = (alt) ? alt : ((alt===null) ? 'really_null' : "");

The desired output from running this code on the 3 tags above is:

text string

really_null

It seems like this should be really easy...but I'm having a really
difficult time trying to figure out what's going on...