Generalized approximate message passing estimation from quantized samples

Ulugbek Kamilov, Vivek K. Goyal, Sundeep Rangan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Estimation of a vector from quantized linear measurements is a common problem for which simple linear techniques are sometimes greatly suboptimal. This paper summarizes the development of generalized approximate message passing (GAMP) algorithms for minimum mean-squared error estimation of a random vector from quantized linear measurements, notably allowing the linear expansion to be overcomplete or undercomplete and the scalar quantization to be regular or non-regular. GAMP is a recently-developed class of algorithms that uses Gaussian approximations in belief propagation and allows arbitrary separable input and output channels. Scalar quantization of measurements is incorporated into the output channel formalism, leading to the first tractable and effective method for high-dimensional estimation problems involving non-regular scalar quantization. Non-regular quantization is empirically demonstrated to greatly improve rate-distortion performance in some problems with oversampling or with undersampling combined with a sparsity-inducing prior. Under the assumption of a Gaussian measurement matrix with i.i.d. entries, the asymptotic error performance of GAMP can be accurately predicted and tracked through the state evolution formalism.

Original languageEnglish (US)
Title of host publication2011 4th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2011
Pages365-368
Number of pages4
DOIs
StatePublished - Dec 1 2011
Event2011 4th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2011 - San Juan, Puerto Rico
Duration: Dec 13 2011Dec 16 2011

Publication series

Name2011 4th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2011

Other

Other2011 4th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2011
CountryPuerto Rico
CitySan Juan
Period12/13/1112/16/11

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ASJC Scopus subject areas

  • Computer Networks and Communications

Cite this

Kamilov, U., Goyal, V. K., & Rangan, S. (2011). Generalized approximate message passing estimation from quantized samples. In 2011 4th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2011 (pp. 365-368). [6136027] (2011 4th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2011). https://doi.org/10.1109/CAMSAP.2011.6136027