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.

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

UR - http://www.scopus.com/inward/citedby.url?scp=85048568614&partnerID=8YFLogxK

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 -