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Title: Signal Recovery and System Calibration from Multiple Compressive Poisson Measurements

Abstract

The measurement matrix employed in compressive sensing typically cannot be known precisely a priori and must be estimated via calibration. One may take multiple compressive measurements, from which the measurement matrix and underlying signals may be estimated jointly. This is of interest as well when the measurement matrix may change as a function of the details of what is measured. This problem has been considered recently for Gaussian measurement noise, and here we develop this idea with application to Poisson systems. A collaborative maximum likelihood algorithm and alternating proximal gradient algorithm are proposed, and associated theoretical performance guarantees are established based on newly derived concentration-of-measure results. A Bayesian model is then introduced, to improve flexibility and generality. Connections between the maximum likelihood methods and the Bayesian model are developed, and example results are presented for a real compressive X-ray imaging system.

Authors:
 [1];  [1];  [1];  [1];  [1];  [2];  [3];  [1];  [1];  [1]
+ Show Author Affiliations
  1. Duke Univ., Durham, NC (United States)
  2. Ecole Polytechnique Federale Lausanne (Switzlerland)
  3. Univ. College London (United Kingdom)
Publication Date:
Research Org.:
Univ. of Michigan, Ann Arbor, MI (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA), Office of Nonproliferation and Verification Research and Development (NA-22)
OSTI Identifier:
1367084
Grant/Contract Number:  
NA0002534
Resource Type:
Accepted Manuscript
Journal Name:
SIAM Journal on Imaging Sciences
Additional Journal Information:
Journal Volume: 8; Journal Issue: 3; Journal ID: ISSN 1936-4954
Country of Publication:
United States
Language:
English
Subject:
47 OTHER INSTRUMENTATION; compressive sensing; Poisson compressive sensing; system calibration; concentration-of-measure; Bayesian compressive sensing; X-ray imaging

Citation Formats

Wang, Liming, Huang, Jiaji, Yuan, Xin, Krishnamurthy, Kalyani, Greenberg, Joel, Cevher, Volkan, Rodrigues, Miguel R. D., Brady, David, Calderbank, Robert, and Carin, Lawrence. Signal Recovery and System Calibration from Multiple Compressive Poisson Measurements. United States: N. p., 2015. Web. doi:10.1137/140998779.
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Wang, Liming, Huang, Jiaji, Yuan, Xin, Krishnamurthy, Kalyani, Greenberg, Joel, Cevher, Volkan, Rodrigues, Miguel R. D., Brady, David, Calderbank, Robert, & Carin, Lawrence. Signal Recovery and System Calibration from Multiple Compressive Poisson Measurements. United States. https://doi.org/10.1137/140998779
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Wang, Liming, Huang, Jiaji, Yuan, Xin, Krishnamurthy, Kalyani, Greenberg, Joel, Cevher, Volkan, Rodrigues, Miguel R. D., Brady, David, Calderbank, Robert, and Carin, Lawrence. Thu . "Signal Recovery and System Calibration from Multiple Compressive Poisson Measurements". United States. https://doi.org/10.1137/140998779. https://www.osti.gov/servlets/purl/1367084.
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@article{osti_1367084,
title = {Signal Recovery and System Calibration from Multiple Compressive Poisson Measurements},
author = {Wang, Liming and Huang, Jiaji and Yuan, Xin and Krishnamurthy, Kalyani and Greenberg, Joel and Cevher, Volkan and Rodrigues, Miguel R. D. and Brady, David and Calderbank, Robert and Carin, Lawrence},
abstractNote = {The measurement matrix employed in compressive sensing typically cannot be known precisely a priori and must be estimated via calibration. One may take multiple compressive measurements, from which the measurement matrix and underlying signals may be estimated jointly. This is of interest as well when the measurement matrix may change as a function of the details of what is measured. This problem has been considered recently for Gaussian measurement noise, and here we develop this idea with application to Poisson systems. A collaborative maximum likelihood algorithm and alternating proximal gradient algorithm are proposed, and associated theoretical performance guarantees are established based on newly derived concentration-of-measure results. A Bayesian model is then introduced, to improve flexibility and generality. Connections between the maximum likelihood methods and the Bayesian model are developed, and example results are presented for a real compressive X-ray imaging system.},
doi = {10.1137/140998779},
journal = {SIAM Journal on Imaging Sciences},
number = 3,
volume = 8,
place = {United States},
year = {Thu Sep 17 00:00:00 EDT 2015},
month = {Thu Sep 17 00:00:00 EDT 2015}
}
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https://doi.org/10.1137/140998779
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