  We study signals that are sparse in graph spectral domain and develop
explicit algorithms to reconstruct the support set as well as partial
components from samples on few vertices of the graph. The number of required
samples is independent of the total size of the graph and takes only local
properties of the graph into account. Our results rely on an operator based
framework for subspace methods and become effective when the spectral
eigenfunctions are zero-free or linear independent on small sets of the
vertices. The latter has recently been adressed using algebraic methods by the
first author.
