Signal Recovery and System Calibration from Multiple Compressive Poisson Measurements

Wang, Liming; Huang, Jiaji; Yuan, Xin; Krishnamurthy, Kalyani; Greenberg, Joel; Cevher, Volkan; Rodrigues, Miguel R.  D.; Brady, David; Calderbank, Robert; Carin, Lawrence

doi:10.1137/140998779

Signal Recovery and System Calibration from Multiple Compressive Poisson Measurements

Journal Article · Thu Sep 17 00:00:00 EDT 2015 · SIAM Journal on Imaging Sciences

DOI:https://doi.org/10.1137/140998779· OSTI ID:1367084

Wang, Liming ^[1]; Huang, Jiaji ^[2]; Yuan, Xin ^[2]; Krishnamurthy, Kalyani ^[2]; Greenberg, Joel ^[2]; Cevher, Volkan ^[3]; Rodrigues, Miguel R. D. ^[4]; Brady, David ^[2]; Calderbank, Robert ^[2]; Carin, Lawrence ^[2]

Duke Univ., Durham, NC (United States); Duke University
Duke Univ., Durham, NC (United States)
Ecole Polytechnique Federale Lausanne (Switzlerland)
Univ. College London (United Kingdom)

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.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Michigan, Ann Arbor, MI (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA), Office of Nonproliferation and Verification Research and Development (NA-22)

Grant/Contract Number:: NA0002534

OSTI ID:: 1367084

Journal Information:: SIAM Journal on Imaging Sciences, Journal Name: SIAM Journal on Imaging Sciences Journal Issue: 3 Vol. 8; ISSN 1936-4954

Country of Publication:: United States

Language:: English

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