  We consider the problem of reconstructing time sequences of spatially sparse
signals (with unknown and time-varying sparsity patterns) from a limited number
of linear "incoherent" measurements, in real-time. The signals are sparse in
some transform domain referred to as the sparsity basis. For a single spatial
signal, the solution is provided by Compressed Sensing (CS). The question that
we address is, for a sequence of sparse signals, can we do better than CS, if
(a) the sparsity pattern of the signal's transform coefficients' vector changes
slowly over time, and (b) a simple prior model on the temporal dynamics of its
current non-zero elements is available. The overall idea of our solution is to
use CS to estimate the support set of the initial signal's transform vector. At
future times, run a reduced order Kalman filter with the currently estimated
support and estimate new additions to the support set by applying CS to the
Kalman innovations or filtering error (whenever it is "large").
