In many applications, the observations can be represented as a signal defined
over the vertices of a graph. The analysis of such signals requires the
extension of standard signal processing tools. In this work, first, we provide
a class of graph signals that are maximally concentrated on the graph domain
and on its dual. Then, building on this framework, we derive an uncertainty
principle for graph signals and illustrate the conditions for the recovery of
band-limited signals from a subset of samples. We show an interesting link
between uncertainty principle and sampling and propose alternative signal
recovery algorithms, including a generalization to frame-based reconstruction
methods. After showing that the performance of signal recovery algorithms is
significantly affected by the location of samples, we suggest and compare a few
alternative sampling strategies. Finally, we provide the conditions for perfect
recovery of a useful signal corrupted by sparse noise, showing that this
problem is also intrinsically related to vertex-frequency localization
properties.Comment: This article is the revised version submitted to the IEEE
Transactions on Signal Processing on May, 2016; first revision was submitted
on January, 2016; original manuscript was submitted on July, 2015. The work
includes 16 pages, 8 figure
