Successful And Failing Matrices For l-1 recovery of sparse vectors

In this thesis we give an overview of the notion of compressed sensing together with some special types of compressed sensing matrices. We then investigate the Restricted Isometry property and the Null Space property which are two of the most well-known properties of compressed sensing matrices needed for sparse signal recovery. We show that when the Restricted Isometry constant is ‘small enough’ then we can recover sparse vectors b