IEEE Transactions on Signal Processing
Sequential detection of targets in multichannel systems
IEEE Transactions on Information Theory
Stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
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We consider the recovery of sparse signals, f ∈ RN, containing at most k ≪ N nonzero entries using linear measurements contaminated with i.i.d. Gaussian background noise. Given this measurement model, we present and analyze a computationally efficient group testing strategy for recovering the support of f and approximating its nonzero entries. In particular, we demonstrate that group testing measurement matrix constructions may be combined with statistical binary detection and estimation methods to produce efficient adaptive sequential algorithms for sparse signal support recovery. Furthermore, when f exhibits sufficient sparsity, we show that these adaptive group testing methods allow the recovery of sparse signals using fewer noisy linear measurements than possible with non-adaptive methods based on Gaussian measurement ensembles. As a result we improve on previous sufficient conditions for sparsity pattern recovery in the noisy sublinear-sparsity regime.