  This paper considers the problem of matrix completion when the observed
entries are noisy and contain outliers. It begins with introducing a new
optimization criterion for which the recovered matrix is defined as its
solution. This criterion uses the celebrated Huber function from the robust
statistics literature to downweigh the effects of outliers. A practical
algorithm is developed to solve the optimization involved. This algorithm is
fast, straightforward to implement, and monotonic convergent. Furthermore, the
proposed methodology is theoretically shown to be stable in a well defined
sense. Its promising empirical performance is demonstrated via a sequence of
simulation experiments, including image inpainting.
