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- W1488456836 abstract "It is well known that ℓ <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> minimization can be used to recover sufficiently sparse unknown signals from compressed linear measurements. In fact, exact thresholds on the sparsity, as a function of the ratio between the system dimensions, so that with high probability almost all sparse signals can be recovered from iid Gaussian measurements, have been computed and are referred to as “weak thresholds”. In this paper, we introduce a reweighted ℓ <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> recovery algorithm composed of two steps: a standard ℓ <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> minimization step to identify a set of entries where the signal is likely to reside, and a weighted ℓ <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> minimization step where entries outside this set are penalized. For signals where the non-sparse component has iid Gaussian entries, we prove a “strict” improvement in the weak recovery threshold. Simulations suggest that the improvement can be quite impressive-over 20% in the example we consider." @default.
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- W1488456836 date "2010-06-01" @default.
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- W1488456836 title "Improved sparse recovery thresholds with two-step reweighted ℓ<inf>1</inf> minimization" @default.
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- W1488456836 doi "https://doi.org/10.1109/isit.2010.5513417" @default.
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