Reconstruction of bathymetries is a key component of shallow water models, which require accurate estimates of both the bottom topography and its spatial derivative. This thesis studies the reconstruction of a one-dimensional bathymetry \(b:[0,1]\to\mathbb{R}\) from incomplete and noisy observations modeled by the linear system \(\mathbf{d} = \mathbf{F}\mathbf{b} + \mathbf{e}\), where \(\mathbf{F}\) is a forward-operator, \(\mathbf{b}\) is the nodal values of \(b\), and \(\mathbf{e}\) is zero-mean Gaussian noise. Two reconstruction approaches are investigated: cubic B-spline interpolation (implemented via package \texttt{TrixiBottomTopography.jl}) and Tikhonov regularization, with the regularization parameter selected by the discrepancy principle. Accuracy is measured on both a smooth and a piecewise smooth synthetic bathymetry using relative errors in the \(\ell_1\), \(\ell_2\), and \(\ell_\infty\) norms, as well as errors in forward-difference derivative estimates. The results indicate that interpolation can be effective for smooth bathymetries but may introduce oscillations, while Tikhonov regularization typically yields smoother and more stable reconstructions. For sparse data with high noise levels, the inverse problem becomes severely ill-posed and accurate recovery cannot be expected without stronger prior assumptions.