Polynomial Accelerated Solutions to a Large Gaussian Model for Imaging Biofilms: In Theory and Finite Precision

• 成果类型: Article
• 署名作者: Parker, Albert E.; Pitts, Betsey; Lorenz, Lindsey; Stewart, Philip S.
• 署名单位: Montana State University System; Montana State University Bozeman; Montana State University System; Montana State University Bozeman; Montana State University System; Montana State University Bozeman
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2017.1409121
• 发表日期: 2018
• 页码: 1431-1442
• 关键词: linear-systems; GIBBS SAMPLER; distributions; relaxation; simulation; variance; gradient

摘要

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. Supplementary materials for this article are available online.