Performance tradeoffs for exact support recovery of sparse signals

We study the tradeoffs between the number of measurements, the signal sparsity level, and the measurement noise level for exact support recovery of sparse signals via random noisy measurements. By drawing analogy between exact support recovery and communication over the Gaussian multiple access channel, and exploiting mathematical tools developed for the latter problem, we derive sharp asymptotic sufficient and necessary conditions for exact support recovery. Specifically, when the number of nonzero entries is held fixed, the exact asymptotics on the number of measurements for support recovery is developed. When the number of nonzero entries increases in certain manners, we obtain sufficient conditions tighter than existing results. The proposed information theoretic framework for analyzing the performance of support recovery is further demonstrated to be capable of dealing with a variety of sparse signal recovery models.