After several years (1997–2001) of industrial research in Hewlett-Packard Lab Israel and in Jigami, Elad took a research associate position at Stanford University from 2001 to 2003, working closely with Prof. Gene Golub (CS-Stanford), Prof. Peyman Milanfar (EE-UCSC) and Prof. David Donoho (Statistics-Stanford).

In 2003, Elad assumed a tenure-track faculty position in the Technion's computer science department.

Among these, he is the creator of the K-SVD algorithm,[1] together with Michal Aharon and Bruckstein, and he is also the author of the 2010 book[2] "Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing".

In 2017, Elad and Yaniv Romano (his PhD student) created a specialized MOOC on sparse representation theory, given under edX.

This is an undergraduate program at the Technion, meant for exceptional students with emphasis on tailored and challenging study tracks.