Compressed Sensing, Group Testing and Matrix Completion in a Nutshell

Compressed sensing of sparse signals is a field that has become pervasive over the last decade, with interesting and strong theoretical guarantees, as well as practical applications across fields. The group testing problem arose several decades earlier in the context of blood testing for syphilis where very few patients had the disease and it was too expensive to test everyone independently. Matrix completion arises naturally in many applications due to incomplete available information. These problems share a lot of ideas, and in this survey we aim to pose the problems in a common framework and discuss the relations between them.