Iterative thresholding algorithms are a class of algorithms well suited for high-dimensional problems in sparse recovery and compressive sensing. Performance of this class of algorithms heavily depends on the tuning of their threshold parameters. In other words, both final reconstruction error and the convergence rate of the algorithm crucially relies on how the threshold parameter is set at each step of the algorithm. In this talk, we propose a parameter-free approximate message passing (AMP) algorithm that sets the threshold parameter at each iteration in a fully automatic way. We show that the proposed method attains both the minimum reconstruction error and the highest convergence rate.