  This paper studies the robust Hankel recovery problem, which simultaneously
removes the sparse outliers and fulfills missing entries from the partial
observation. We propose a novel non-convex algorithm, coined Hankel Structured
Newton-Like Descent (HSNLD), to tackle the robust Hankel recovery problem.
HSNLD is highly efficient with linear convergence, and its convergence rate is
independent of the condition number of the underlying Hankel matrix. The
recovery guarantee has been established under some mild conditions. Numerical
experiments on both synthetic and real datasets show the superior performance
of HSNLD against state-of-the-art algorithms.
