  A noise-corrupted image often requires interpolation. Given a linear denoiser
and a linear interpolator, when should the operations be independently executed
in separate steps, and when should they be combined and jointly optimized? We
study joint denoising / interpolation of images from a mixed graph filtering
perspective: we model denoising using an undirected graph, and interpolation
using a directed graph. We first prove that, under mild conditions, a linear
denoiser is a solution graph filter to a maximum a posteriori (MAP) problem
regularized using an undirected graph smoothness prior, while a linear
interpolator is a solution to a MAP problem regularized using a directed graph
smoothness prior. Next, we study two variants of the joint interpolation /
denoising problem: a graph-based denoiser followed by an interpolator has an
optimal separable solution, while an interpolator followed by a denoiser has an
optimal non-separable solution. Experiments show that our joint denoising /
interpolation method outperformed separate approaches noticeably.
