  Dynamic robust PCA refers to the dynamic (time-varying) extension of robust
PCA (RPCA). It assumes that the true (uncorrupted) data lies in a
low-dimensional subspace that can change with time, albeit slowly. The goal is
to track this changing subspace over time in the presence of sparse outliers.
We develop and study a novel algorithm, that we call simple-ReProCS, based on
the recently introduced Recursive Projected Compressive Sensing (ReProCS)
framework. Our work provides the first guarantee for dynamic RPCA that holds
under weakened versions of standard RPCA assumptions, slow subspace change and
a lower bound assumption on most outlier magnitudes. Our result is significant
because (i) it removes the strong assumptions needed by the two previous
complete guarantees for ReProCS-based algorithms; (ii) it shows that it is
possible to achieve significantly improved outlier tolerance, compared with all
existing RPCA or dynamic RPCA solutions by exploiting the above two simple
extra assumptions; and (iii) it proves that simple-ReProCS is online (after
initialization), fast, and, has near-optimal memory complexity.
