Approximate Message Passing with Parameter Estimation: a probabilistic Bayesian dipole inversion. MAP estimation over the nonlinear complex-exponential forward model with a Laplace sparse-wavelet prior and a two-component Gaussian-mixture noise model, with all distribution parameters estimated automatically (tuning-free). Compiled from MATLAB and run on the license-free MATLAB Runtime. QSM-CI reconstruction method amp-pe. Browse and run it at https://qsmxt.github.io/QSM-CI/submission.html?method=amp-pe.