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Abstract: We consider the problem of exact support recovery of sparse signals via noisymeasurements. The main focus is the sufficient and necessary conditions on thenumber of measurements for support recovery to be reliable. By drawing ananalogy between the problem of support recovery and the problem of channelcoding over the Gaussian multiple access channel, and exploiting mathematicaltools developed for the latter problem, we obtain an information theoreticframework for analyzing the performance limits of support recovery. Sharpsufficient and necessary conditions on the number of measurements in terms ofthe signal sparsity level and the measurement noise level are derived.Specifically, when the number of nonzero entries is held fixed, the exactasymptotics on the number of measurements for support recovery is developed.When the number of nonzero entries increases in certain manners, we obtainsufficient conditions tighter than existing results. In addition, we show thatthe proposed methodology can deal with a variety of models of sparse signalrecovery, hence demonstrating its potential as an effective analytical tool.



Author: Yuzhe Jin, Young-Han Kim, Bhaskar D. Rao

Source: https://arxiv.org/







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