VECTOR APPROXIMATE MESSAGE PASSING FOR QUANTIZED COMPRESSED SENSING

In recent years approximate message passing algorithms have gained a lot of attention and different versions have been proposed for coping with various system models. This paper focuses on vector approximate message passing (VAMP) for generalized linear models. While this algorithm is originally derived from a message passing point of view, we will review it from an estimation theory perspective and afterwards adapt it for a quantized compressed sensing application. Finally, numerical results are presented to evaluate the performance of the algorithm.

[1]  Steven Kay,et al.  Fundamentals Of Statistical Signal Processing , 2001 .

[2]  J. W. Silverstein,et al.  On the empirical distribution of eigenvalues of a class of large dimensional random matrices , 1995 .

[3]  Laurent Jacques,et al.  Quantization and Compressive Sensing , 2014, ArXiv.

[4]  Sundeep Rangan,et al.  Message-Passing De-Quantization With Applications to Compressed Sensing , 2012, IEEE Transactions on Signal Processing.

[5]  Laurent Jacques,et al.  Quantized Iterative Hard Thresholding: Bridging 1-bit and High-Resolution Quantized Compressed Sensing , 2013, ArXiv.

[6]  Sundeep Rangan,et al.  Generalized approximate message passing for estimation with random linear mixing , 2010, 2011 IEEE International Symposium on Information Theory Proceedings.

[7]  Rangan Sundeep,et al.  Vector approximate message passing for the generalized linear model , 2016 .

[8]  Deanna Needell,et al.  Methods for quantized compressed sensing , 2015, 2016 Information Theory and Applications Workshop (ITA).

[9]  Richard G. Baraniuk,et al.  1-Bit compressive sensing , 2008, 2008 42nd Annual Conference on Information Sciences and Systems.

[10]  Robert F. H. Fischer,et al.  Unveiling bias compensation in turbo-based algorithms for (discrete) compressed sensing , 2017, 2017 25th European Signal Processing Conference (EUSIPCO).

[11]  Sundeep Rangan,et al.  Vector approximate message passing , 2017, 2017 IEEE International Symposium on Information Theory (ISIT).