A total variation regularization method for an inverse problem of recovering an unknown diffusion coefficient in a parabolic equation

Figures & data

Figure 1. A target node o and its neighbours, the spatial step size is h.

Figure 2. Reconstructions of the coefficient $k(x)$ in example 1, $k^{(0)}(x)=1$, $\lambda =0.005$.

Figure 3. Reconstructions of the coefficient $k(x)$ in example 2, $k^{(0)}(x)=1$, $\lambda =0.05$.

Figure 4. Reconstructions of the coefficient $k(x)$ in example 3, $k^{(0)}(x)=1$, $\lambda =0.01$.