  In this work we introduce the concept of $s$-sparse observability for large
systems of ordinary differential equations. Let $\dot x=f(t,x)$ be such a
system. At time $T>0$, suppose we make a set of observations $b=Ax(T)$ of the
solution of the system with initial data $x(0)=x^0$, where $A$ is a matrix
satisfying the restricted isometry property. The aim of this paper is to give
answers to the following questions: Given the observations $b$, is $x^0$
uniquely determined knowing that $x^0$ is sufficiently sparse? Is there any way
to reconstruct such a sparse initial data $x^0$?
