  We propose a time-varying graph signal recovery method for estimating the
true time-varying graph signal from observations that are corrupted by missing
values, unknown position outliers, and some random noise. Most existing studies
on time-varying graph signal recovery focus on online estimation and graph
learning based on the assumption that the entire dynamic graphs are not
available, and robust recovery formulations and algorithms that fully exploit
the entire dynamically changing graph structure have not been well studied. On
the other hand, there are many situations, especially when dealing with
timevarying data obtained from physical sensor networks, where the appropriate
dynamic graphs can be easily generated using simple algorithms such as
k-nearest neighbor by exploiting information on time-varying spatial sensor
locations. In this paper, we focus on such cases and formulate dynamic graph
signal recovery as a constrained convex optimization problem that
simultaneously estimates both time-varying graph signals and sparsely modeled
outliers. In our formulation, we use two types of regularizations, time-varying
graph Laplacian-based and temporal differencebased, and also separately modeled
missing values with known positions and unknown outliers, to achieve robust
estimation from highly degraded data. In addition, an algorithm is developed to
efficiently solve the optimization problem based on a primaldual splitting
method. Extensive experiments on simulated drone remote sensing data and real
sea surface temperature distribution data demonstrate the advantages of the
proposed method over existing methods.

Signal Processing