point $z$, the reconstructed function $f(z)$ is also a Gaussian distribution with a mean value and Gaussian error. In this process, the values of the reconstructed function evaluated at any two different points $z$ and $\tilde{z}$, are connected by a covariance function $k(z,\tilde{z})$. In this paper, we take the Matérn ($\nu = 9/2$) covariance function $$\begin{aligned}
k(z,\tilde z) = &~{\sigma _f}^2\exp\left( - \frac{{3\left| {z - \tilde z} \right|}}{\ell }\right) \nonumber \\
      &~~\times\Big[1 + \frac{{3\left| {z - \tilde z} \right|}}{\ell } + \frac{{27{{(z - \tilde z)}^2}}}{{7{\ell ^2}}} \nonumber \\
     &~~ + \frac{{18{{\left| {z - \tilde z} \right|}^3}}}{{7{\ell ^3}}} + \frac{{27{{(z - \tilde z)}^4}}}{{35{\ell ^4}}}\Big],\end{aligned}$$ where $\ell$ provides a measure of the coherence length of the correlation in $x$-direction and $\sigma_f$ is the overall amplitude of the correlation in the $y$-direction. The values of the two hyper parameters $\sigma_f$ and $\ell$ will be optimized by GP with the observed data set. This implies that the reconstructed function is not dependent on the initial hyper-parameter settings, which guarantees the reliability of the reconstructed function. Compared with the squared exponential form for covariance function, which has been widely used in the literature [@Seikel12a; @Seikel12b; @Cai; @Yennapureddy; @Melia18b], the Matérn ($\nu=9/2$) covariance function can lead 