Polynomial accelerated solutions to a LARGE Gaussian model for imaging biofilms: in theory and finite precision
Date
2018-06Metadata
Show full item recordAbstract
Three-dimensional confocal scanning laser microscope images offer dramatic visualizations of living
biofilms before and after interventions. Here, we use confocal microscopy to study the effect of a treatment
over time that causes a biofilm to swell and contract due to osmotic pressure changes. From these
data (the video is provided in the supplementary materials), our goal is to reconstruct biofilm surfaces, to
estimate the effect of the treatment on the biofilm’s volume, and to quantify the related uncertainties. We
formulate the associated massive linear Bayesian inverse problem and then solve it using iterative samplers
from large multivariate Gaussians that exploit well-established polynomial acceleration techniques from
numerical linear algebra. Because of a general equivalence with linear solvers, these polynomial accelerated
iterative samplers have known convergence rates, stopping criteria, and perform well in finite precision. An
explicit algorithm is provided, for the first time, for an iterative sampler that is accelerated by the synergistic
implementation of preconditioned conjugate gradient and Chebyshev polynomials.
Citation
Parker, Albert E., Betsey Pitts, Lindsey Lorenz, and Philip S. Stewart. “Polynomial Accelerated Solutions to a Large Gaussian Model for Imaging Biofilms: In Theory and Finite Precision.” Journal of the American Statistical Association (June 28, 2018), 113(524):1431-1442.