  We propose and analyze an online algorithm for reconstructing a sequence of
signals from a limited number of linear measurements. The signals are assumed
sparse, with unknown support, and evolve over time according to a generic
nonlinear dynamical model. Our algorithm, based on recent theoretical results
for $\ell_1$-$\ell_1$ minimization, is recursive and computes the number of
measurements to be taken at each time on-the-fly. As an example, we apply the
algorithm to compressive video background subtraction, a problem that can be
stated as follows: given a set of measurements of a sequence of images with a
static background, simultaneously reconstruct each image while separating its
foreground from the background. The performance of our method is illustrated on
sequences of real images: we observe that it allows a dramatic reduction in the
number of measurements with respect to state-of-the-art compressive background
subtraction schemes.
