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Observed phase transitions of reconstruction algorithms. Red curve, AMP; green curve, iterative soft thresholding (IST); blue curve, theoretical ℓ1 transition. Parameters of IST tuned for best possible phase transition (3). Reconstruction signal length N = 1,000. T = 1,000 iterations. Empirical phase transition is value of ρ at which success rate is 50%. Details are in SI Appendix.
