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This paper considers the reconstruction of non-uniformly sparse signals from noisy linear observations. By non-uniformly sparse, we mean that the signal coefficients can be partitioned into subsets that differ in the rate at which the coefficients tend to be active (i.e., nonzero). Inspired by recent work of Donoho, Maleki, and Montanari, we design a minimax-optimal approximate message passing (AMP)...
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