Signal recovery and system calibration from multiple compressive poisson measurements

Published

Journal Article

© 2015 Society for Industrial and Applied Mathematics. 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.

Full Text

Duke Authors

Cited Authors

  • Wang, L; Huang, J; Yuan, X; Krishnamurthy, K; Greenberg, J; Cevher, V; Rodrigues, MRD; Brady, D; Calderbank, R; Carin, L

Published Date

  • September 17, 2015

Published In

Volume / Issue

  • 8 / 3

Start / End Page

  • 1923 - 1954

Electronic International Standard Serial Number (EISSN)

  • 1936-4954

Digital Object Identifier (DOI)

  • 10.1137/140998779

Citation Source

  • Scopus