Is there a classification of closed self-dual 4-manifolds with positive sectional curvature?

In a paper of LeBrun-Nayatani-Nitta, they proved that a compact self-dual 4-manifold with positive Ricci curvature is homeomorphic to $n\,\mathbf{CP}^2$ for some $n \geq 0$, and diffeomorphic to $n\,\mathbf{CP}^2$ if $n \leq 4$.

I was wondering: is there a classification of compact self-dual 4-manifolds with positive sectional curvature? Thank you.

-
It is possible that this paper of LeBrun is very well known. But in general please try to provide either the citation information or an internet link when you ask about "a paper" on MO. Thanks! –  Willie Wong Aug 14 at 13:12
Sorry for the inconvenience, I added LeBrun's paper. –  user38600 Aug 14 at 13:14