  This paper presents results pertaining to sequential methods for support
recovery of sparse signals in noise. Specifically, we show that any sequential
measurement procedure fails provided the average number of measurements per
dimension grows slower then log s / D(f0||f1) where s is the level of sparsity,
and D(f0||f1) the Kullback-Leibler divergence between the underlying
distributions. For comparison, we show any non-sequential procedure fails
provided the number of measurements grows at a rate less than log n /
D(f1||f0), where n is the total dimension of the problem. Lastly, we show that
a simple procedure termed sequential thresholding guarantees exact support
recovery provided the average number of measurements per dimension grows faster
than (log s + log log n) / D(f0||f1), a mere additive factor more than the
lower bound.
