Sampling and reconstructing diffusion fields in presence of aliasing

The reconstruction of a diffusion field, such as temperature, from samples collected by a sensor network is a classical inverse problem and it is known to be ill-conditioned. Previous work considered source models, such as sparse sources, to regularize the solution. Here, we consider uniform spatial sampling and reconstruction by classical interpolation techniques for those scenarios where the spatial sparsity of the sources is not realistic. We show that even if the spatial bandwidth of the field is infinite, we can exploit the natural low-pass filter given by the diffusion phenomenon to bound the aliasing error.