Chapter 17: AMP and OAMP for RF Imaging

Learning Objectives

• Recap the AMP iteration and its Onsager correction, and explain precisely why AMP fails for structured sensing matrices
• Derive OAMP/VAMP as the principled fix for non-i.i.d. matrices, identifying the orthogonality condition and its enforcement via the LMMSE step
• Exploit Kronecker structure in the RF imaging operator to reduce the LMMSE complexity from cubic in the product dimension to cubic in the factor dimensions
• Design and compare denoisers for the imaging OAMP loop — soft thresholding, BG-MMSE, and learned denoisers (DnCNN, U-Net)
• Analyze mismatch between assumed and true signal priors within the OAMP state-evolution framework