  Key to successfully deal with complex contemporary datasets is the
development of tractable models that account for the irregular structure of the
information at hand. This paper provides a comprehensive and unifying view of
several sampling, reconstruction, and recovery problems for signals defined on
irregular domains that can be accurately represented by a graph. The workhorse
assumption is that the (partially) observed signals can be modeled as the
output of a graph filter to a structured (parsimonious) input graph signal.
When either the input or the filter coefficients are known, this is tantamount
to assuming that the signals of interest live on a subspace defined by the
supporting graph. When neither is known, the model becomes bilinear. Upon
imposing different priors and additional structure on either the input or the
filter coefficients, a broad range of relevant problem formulations arise. The
goal is then to leverage those priors, the shift operator of the supporting
graph, and the samples of the signal of interest to recover: the signal at the
non-sampled nodes (graph-signal interpolation), the input (deconvolution), the
filter coefficients (system identification), or any combination thereof (blind
deconvolution).
