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Compressed Sensing with Quantized Measurements

Argyrios Zymnis (azymnis***at***stanford.edu)
Stephen Boyd (boyd***at***stanford.edu)
Emmanuel Candes (emmanuel***at***acm.caltech.edu)

Abstract: We consider the problem of estimating a sparse signal from a set of quantized, Gaussian noise corrupted measurements, where each measurement corresponds to an interval of values. We give two methods for (approximately) solving this problem, each based on minimizing a differentiable convex function plus an l1 regularization term. Using a first order method developed by Yin et al, we demonstrate the performance of the methods through numerical simulation. We find that, using these methods, compressed sensing can be carried out even when the quantization is very coarse, e.g., 1 or 2 bits per measurement.

Keywords: compressed sensing, statistical signal processing

Category 1: Applications -- Science and Engineering (Statistics )

Citation: Available online at: http://stanford.edu/~boyd/papers/quant_compr_sens.html

Download: [PDF]

Entry Submitted: 04/24/2009
Entry Accepted: 04/24/2009
Entry Last Modified: 04/28/2009

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