The prices of call options in a certain local volatility model of the form $d S_{t}=S_{t} \sigma\left(t, S_{t}ight) d B_{t}$ with risk-free rate $\underline{r=0}$ are given by

$$
C\left(S_{0}, K, Tight)=\sqrt{\frac{T}{2 \pi}} \mathrm{e}^{-\left(K-S_{0}ight)^{2} /(2 T)}-\left(K-S_{0}ight) \Phi\left(-\frac{K-S_{0}}{\sqrt{T}}ight), \quad K, T>0 .
$$

Recover the local volatility function $\sigma(t, x)$ of this model by applying the Dupire formula.