  In this note, we investigate the theoretical properties of Orthogonal
Matching Pursuit (OMP), a class of decoder to recover sparse signal in
compressed sensing. In particular, we show that the OMP decoder can give
$(p,q)$ instance optimality for a large class of encoders with $1\leq p\leq q
\leq 2$ and $(p,q)\neq (2,2)$. We also show that, if the encoding matrix is
drawn from an appropriate distribution, then the OMP decoder is $(2,2)$
instance optimal in probability.
