  This paper designs and evaluates a practical algorithm, called practical
recursive projected compressive sensing (Prac-ReProCS), for recovering a time
sequence of sparse vectors $S_t$ and a time sequence of dense vectors $L_t$
from their sum, $M_t:= S_t + L_t$, when any subsequence of the $L_t$'s lies in
a slowly changing low-dimensional subspace. A key application where this
problem occurs is in video layering where the goal is to separate a video
sequence into a slowly changing background sequence and a sparse foreground
sequence that consists of one or more moving regions/objects. Prac-ReProCS is a
practical modification of its theoretical counterpart which was analyzed in our
recent work. Experimental comparisons demonstrating the advantage of the
approach for both simulated and real videos are shown. Extension to the
undersampled case is also developed.
