Adaptive smoothing of the log-sum penalty in AMP widens the exact-recovery phase transition in compressed sensing past l1, per replica and state-evolution analysis, but metastable states prevent the Bayes-optimal limit.
Chartrand, IEEE Signal Processing Letters14, 707 (2007)
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Phase transition in compressed sensing using log-sum penalty and adaptive smoothing
Adaptive smoothing of the log-sum penalty in AMP widens the exact-recovery phase transition in compressed sensing past l1, per replica and state-evolution analysis, but metastable states prevent the Bayes-optimal limit.