We design an algorithm based on IRL1 that, independently of the initialization x0 , provably reconstructs x⋆ ; in addition, it automatically selects the number of measurements m, via a feedback mechanism between the encoder and the decoder. Experiments show that our algorithm adds no significant computation with respect to IRL1, but the number of measurements that it selects is often smaller than the number of measurements that IRL1 requires,even when we know the exact phase transition of IRL1.