Parametric Bilinear Generalized Approximate Message Passing by Jason T. Parker, Yan Shou, Philip Schniter

We propose a scheme to estimate the parametersbi andcj of the bilinear formzm=∑i,jbiz(i,j)mcj from noisy measurements{ym}Mm=1 , whereym andzm are related through an arbitrary likelihood function andz(i,j)m are known. Our scheme is based on generalized approximate message passing (G-AMP): it treatsbi andcj as random variables andz(i,j)m as an i.i.d.\ Gaussian tensor in order to derive a tractable simplification of the sum-product algorithm in the large-system limit. It generalizes previous instances of bilinear G-AMP, such as those that estimate matricesB andC from a noisy measurement ofZ=BC , allowing the application of AMP methods to problems such as self-calibration, blind deconvolution, and matrix compressive sensing. Numerical experiments confirm the accuracy and computational efficiency of the proposed approach.

The implementation can be found here: http://gampmatlab.wikia.com/wiki/Generalized_Approximate_Message_Passing

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