Chapter 20: Approximate Message Passing (AMP)

Learning Objectives

• Derive the AMP iteration from the TAP equations and explain the role of the Onsager correction term
• State and apply the scalar state evolution recursion to predict AMP's per-iteration MSE
• Identify the phase transition boundary for sparse recovery from state-evolution fixed points
• Design denoisers (soft-thresholding, MMSE, learned) and link them to LASSO and Bayes-optimal estimation
• Diagnose AMP failure modes under structured sensing matrices and understand why damping is a palliative rather than a cure