  In this work, we obtain performance guarantees for modified-CS and for its
improved version, modified-CS-Add-LS-Del, for recursive reconstruction of a
time sequence of sparse signals from a reduced set of noisy measurements
available at each time. Under mild assumptions, we show that the support
recovery error of both algorithms is bounded by a time-invariant and small
value at all times. The same is also true for the reconstruction error. Under a
slow support change assumption, (i) the support recovery error bound is small
compared to the support size; and (ii) our results hold under weaker
assumptions on the number of measurements than what $\ell_1$ minimization for
noisy data needs. We first give a general result that only assumes a bound on
support size, number of support changes and number of small magnitude nonzero
entries at each time. Later, we specialize the main idea of these results for
two sets of signal change assumptions that model the class of problems in which
a new element that is added to the support either gets added at a large initial
magnitude or its magnitude slowly increases to a large enough value within a
finite delay. Simulation experiments are shown to back up our claims.
