Measurements vs. Bits: Compressed Sensing meets Information Theory

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Title: Measurements vs. Bits: Compressed Sensing meets Information Theory
Author: Sarvotham, Shriram; Baron, Dror; Baraniuk, Richard G.
Type: Conference Paper
Keywords: Compressed sensing; information theory
Citation: S. Sarvotham, D. Baron and R. G. Baraniuk,"Measurements vs. Bits: Compressed Sensing meets Information Theory," in Allerton Conference on Communication, Control and Computing,
Abstract: Compressed sensing is a new framework for acquiring sparse signals based on the revelation that a small number of linear projections (measurements) of the signal contain enough information for its reconstruction. The foundation of Compressed sensing is built on the availability of noise-free measurements. However, measurement noise is unavoidable in analog systems and must be accounted for. We demonstrate that measurement noise is the crucial factor that dictates the number of measurements needed for reconstruction. To establish this result, we evaluate the information contained in the measurements by viewing the measurement system as an information theoretic channel. Combining the capacity of this channel with the rate-distortion function of the sparse signal, we lower bound the rate-distortion performance of a compressed sensing system. Our approach concisely captures the effect of measurement noise on the performance limits of signal reconstruction, thus enabling to benchmark the performance of specific reconstruction algorithms.
Date Published: 2006-09-01

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  • ECE Publications [1082 items]
    Publications by Rice University Electrical and Computer Engineering faculty and graduate students
  • DSP Publications [508 items]
    Publications by Rice Faculty and graduate students in digital signal processing.