Reproducible code and data are available at Github. work Quantitative MRI The mono-exponential decay model of MR signal is incorporated into a Bayesian approach to recover the R2* map via compressive sensing Quantitative Susceptibility Mapping A bespoke Gaussian-mixture distribution is used to model the long-tailed noise distribution in cases of brain hemorrhage and/or calcification QSM. Cryo-electron Microscopy Reconstruct 3D protein density model fraom random 2D projections with unknown viewing angles. Nonconvex Quadratic System Convergence analysis around the global optimum of nonconvex quadratic system Generalized Entropy Functions Minimizing the generalized entropy function for sparse signal recovery Approximate Message Passing Bayesian methods for sparse signal recovery with automatic hyperparameter estimation