Signal recovery and system calibration from multiple compressive poisson measurements

TitleSignal recovery and system calibration from multiple compressive poisson measurements
Publication TypeJournal Article
Year of Publication2015
AuthorsL Wang, J Huang, X Yuan, K Krishnamurthy, J Greenberg, V Cevher, MRD Rodrigues, D Brady, R Calderbank, and L Carin
JournalSiam Journal on Imaging Sciences
Volume8
Start Page1923
Issue3
Pagination1923 - 1954
Date Published09/2015
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.

DOI10.1137/140998779
Short TitleSiam Journal on Imaging Sciences