Abstract blowing down

Assume that $X$ is a surface over an algebraically closed field $k$. Let $\tilde{X}$ be obtained from $X$ by blowing up a smooth point and let $L$ be the exceptional curve. Let $\operatorname{coh}(X)$ be the category of coherent sheaves on $X$. In this note we show how to recover $\operatorname{coh}({X})$ from $\operatorname{coh}(\tilde{X})$, if we know the object $\mathcal{O}_L(L)$.