I am looking for references discussing the formal requirements for the dimension $m$ of the "measurement" mixing matrix (as in ${\bf y} = M {\bf x}$ where ${\bf y} \in \mathbb{R}^ m$ and $ M \in \mathbb{R}^{ m \times n}$ with $m < n$). Question: What is the "smallest" dimension $m$, as related to the simple "sparsity measure" (i.e. 90% of entries are zero) of the original signal $\bf x$? Any references would be greatly helpful.