References & Further Reading

References

J. Ma and L. Ping, Orthogonal AMP, 2017
Introduces OAMP. Enforces a divergence-free condition on both the linear and denoising steps so that state evolution survives for the right-rotationally-invariant matrix class.
S. Rangan, P. Schniter, and A. K. Fletcher, Vector Approximate Message Passing, 2019
Derives VAMP via expectation consistency. Proves state evolution for right-rotationally-invariant sensing matrices and establishes Bayes-optimality under matched priors.
M. Opper and O. Winther, Expectation Consistent Approximate Inference, 2005
The statistical-physics origin of the expectation-consistent framework from which VAMP was later rediscovered.
S. Rangan, Generalized Approximate Message Passing for Estimation with Random Linear Mixing, 2011
Extends AMP to generalized linear models. Introduces the two-variance (input / output) state evolution that handles non-Gaussian likelihoods such as Poisson and 1-bit CS.
L. Jacques, J. N. Laska, P. T. Boufounos, and R. G. Baraniuk, Robust 1-Bit Compressive Sensing via Binary Stable Embeddings of Sparse Vectors, 2013
Formalises 1-bit compressed sensing, proves stable-embedding guarantees, and motivates the output-denoiser family used by 1-bit GAMP.
J. P. Vila and P. Schniter, Expectation-Maximization Gaussian-Mixture Approximate Message Passing, 2013
EM-GAMP: automatic hyperparameter tuning for GAMP via expectation-maximisation updates of the prior and noise parameters. Makes GAMP parameter-free in practice.
K. Takeuchi, On the Convergence of Orthogonal/Vector AMP: Long-Memory Message-Passing Strategy, 2022
Rigorous analysis of mismatch in OAMP/VAMP: how incorrect assumed prior / noise parameters propagate through state evolution and how long-memory variants mitigate the damage.
M. F. Hutchinson, A Stochastic Estimator of the Trace of the Influence Matrix for Laplacian Smoothing Splines, 1990
The original stochastic trace estimator, used in OAMP/VAMP to estimate $\mathrm{tr}(\mathbf{W}\ntn{sens})$ without forming the full matrix product.
K. Gregor and Y. LeCun, Learning Fast Approximations of Sparse Coding, 2010
Introduces LISTA — the first deep-unfolding paper. Trains a fixed-depth network whose layers mimic ISTA iterations.
M. Borgerding, P. Schniter, and S. Rangan, AMP-Inspired Deep Networks for Sparse Linear Inverse Problems, 2017
LAMP and LDVAMP: unrolled AMP / VAMP networks with learnable feedback matrices, denoiser parameters, and Onsager coefficients. Benchmarks against fixed-parameter baselines.
C. A. Metzler, A. Mousavi, and R. G. Baraniuk, Learned D-AMP: Principled Neural Network Based Compressive Image Recovery, 2017
Learned Denoising AMP: wraps a CNN denoiser inside an AMP loop, with Monte-Carlo divergence estimation, for image recovery.
P. Schniter, S. Rangan, and A. K. Fletcher, Vector Approximate Message Passing for the Generalized Linear Model, 2016
Extends VAMP to the generalized-linear-model setting, merging the strengths of VAMP (RRI robustness) and GAMP (non-Gaussian likelihoods).
K. Takeuchi, Rigorous Dynamics of Expectation-Propagation-Based Signal Recovery from Unitarily Invariant Measurements, 2017
Rigorous proof of OAMP/VAMP state evolution for unitarily-invariant matrices using the conditional- distribution argument.
A. Javanmard and A. Montanari, State Evolution for General Approximate Message Passing Algorithms, with Applications to Spatial Coupling, 2013
Rigorous state-evolution proof for generalised AMP iterations, covering GAMP and spatially coupled constructions.
M. Dehkordi, P. Jung, G. Caire, Unrolled OAMP with Kronecker Structure for Distributed RF Imaging, 2023