Typical Performance of Iterative Reweighted Lasso for Compressed Sensing

The iterative reweighted Lasso is an efficient framework to recover a sparse signal from a noisy linear measurement. Applying the statistical mechanical approach, we investigate the performance of the iterative reweighted Lasso by evaluating the mean squared error of the estimates. Regions where the reweighting becomes effective are revealed. Our analysis allows us to investigate property of functions that define the weight.