Critical compression ratio of iterative reweighted l1 minimization for compressed sensing

ℓ₁ minimization for compressed sensing provides a computationally efficient means to reconstruct sparse signals from linear measurements whose number is less than the dimension of the signal. Reconstruction from a smaller number of measurements can be possible via iterative reweighted ℓ₁ minimization (IRL1). In this paper, adopting a statistical-mechanics approach, we propose an analytical framework for evaluating critical compression ratio, the ratio of the number of measurements to the dimension of the signal, for IRL1.