  In this paper we consider the problem of exact recovery of a fixed sparse
vector with the measurement matrices sequentially arriving along with
corresponding measurements. We propose an extension of the iterative hard
thresholding (IHT) algorithm, termed as sequential IHT (SIHT) which breaks the
total time horizon into several phases such that IHT is executed in each of
these phases using a fixed measurement matrix obtained at the beginning of that
phase. We consider a stochastic setting where the measurement matrices obtained
at each phase are independent samples of a sub Gaussian random matrix. We prove
that if a certain dynamic sample complexity that depends on the sizes of the
measurement matrices at each phase, along with their duration and the number of
phases, satisfy certain lower bound, the estimation error of SIHT over a fixed
time horizon decays rapidly. Interestingly, this bound reveals that the
probability of decay of estimation error is hardly affected even if very small
number measurements are sporadically used in different phases. This theoretical
observation is also corroborated using numerical experiments demonstrating that
SIHT enjoys improved probability of recovery compared to offline IHT.
