  We investigate a diffusion process in heterogeneous media where particles
stochastically reset to their initial positions at a constant rate. The
heterogeneous media is modeled using a spatial-dependent diffusion coefficient
with a power-law dependence on particles' positions. We use the Green function
approach to obtain exact solutions for the probability distribution of
particles' positions and the mean square displacement. These results are
further compared and agree with numerical simulations of a Langevin equation.
We also study the first-passage time problem associated with this diffusion
process and obtain an exact expression for the mean first-passage time. Our
findings show that this system exhibits non-Gaussian distributions, transient
anomalous diffusion (sub- or superdiffusion) and stationary states that
simultaneously depend on the media heterogeneity and the resetting rate. We
further demonstrate that the media heterogeneity non-trivially affect the mean
first-passage time, yielding an optimal resetting rate for which this quantity
displays a minimum.
