The null space property for sparse recovery from multiple measurement vectors

We prove a null space property for the uniqueness of the sparse solution vectors recovered from a minimization in ℓp quasi-norm subject to multiple systems of linear equations, where p∈(0,1]. Furthermore, we show that the null space property is equivalent to the null space property for the standard ℓp minimization subject to a single linear system. This answers the questions raised in Foucart and Gribonval (2010) [17].