TY - GEN
T1 - An expectation-maximization approach to tuning generalized vector approximate message passing
AU - Metzler, Christopher A.
AU - Schniter, Philip
AU - Baraniuk, Richard G.
N1 - Publisher Copyright:
© Springer International Publishing AG, part of Springer Nature 2018.
PY - 2018
Y1 - 2018
N2 - Generalized Vector Approximate Message Passing (GVAMP) is an efficient iterative algorithm for approximately minimum-mean-squared-error estimation of a random vector x~px(x) from generalized linear measurements, i.e., measurements of the form y=Q(z) where z = Ax with known A, and Q(·) is a noisy, potentially nonlinear, componentwise function. Problems of this form show up in numerous applications, including robust regression, binary classification, quantized compressive sensing, and phase retrieval. In some cases, the prior p(x) and/or channel Q(·) depend on unknown deterministic parameters θ, which prevents a direct application of GVAMP. In this paper we propose a way to combine expectation maximization (EM) with GVAMP to jointly estimate x and θ. We then demonstrate how EM-GVAMP can solve the phase retrieval problem with unknown measurement-noise variance.
AB - Generalized Vector Approximate Message Passing (GVAMP) is an efficient iterative algorithm for approximately minimum-mean-squared-error estimation of a random vector x~px(x) from generalized linear measurements, i.e., measurements of the form y=Q(z) where z = Ax with known A, and Q(·) is a noisy, potentially nonlinear, componentwise function. Problems of this form show up in numerous applications, including robust regression, binary classification, quantized compressive sensing, and phase retrieval. In some cases, the prior p(x) and/or channel Q(·) depend on unknown deterministic parameters θ, which prevents a direct application of GVAMP. In this paper we propose a way to combine expectation maximization (EM) with GVAMP to jointly estimate x and θ. We then demonstrate how EM-GVAMP can solve the phase retrieval problem with unknown measurement-noise variance.
KW - Compressive sensing
KW - Expectation maximization
KW - Generalized linear model
KW - Phase retrieval
UR - http://www.scopus.com/inward/record.url?scp=85048568614&partnerID=8YFLogxK
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U2 - 10.1007/978-3-319-93764-9_37
DO - 10.1007/978-3-319-93764-9_37
M3 - Conference contribution
AN - SCOPUS:85048568614
SN - 9783319937632
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 395
EP - 406
BT - Latent Variable Analysis and Signal Separation - 14th International Conference, LVA/ICA 2018, Proceedings
A2 - Gannot, Sharon
A2 - Deville, Yannick
A2 - Mason, Russell
A2 - Plumbley, Mark D.
A2 - Ward, Dominic
PB - Springer-Verlag
T2 - 14th International Conference on Latent Variable Analysis and Signal Separation, LVA/ICA 2018
Y2 - 2 July 2018 through 5 July 2018
ER -