  In this letter, we study the deterministic sampling patterns for the
completion of low rank matrix, when corrupted with a sparse noise, also known
as robust matrix completion. We extend the recent results on the deterministic
sampling patterns in the absence of noise based on the geometric analysis on
the Grassmannian manifold. A special case where each column has a certain
number of noisy entries is considered, where our probabilistic analysis
performs very efficiently. Furthermore, assuming that the rank of the original
matrix is not given, we provide an analysis to determine if the rank of a valid
completion is indeed the actual rank of the data corrupted with sparse noise by
verifying some conditions.
