Polynomial Accelerated Solutions to a Large Gaussian Model for Imaging Biofilms: In Theory and Finite Precision
利用共聚焦显微镜数据，通过多项式加速迭代采样器求解大规模线性贝叶斯逆问题，重建生物膜表面并估计体积变化及不确定性，对生物膜研究和图像处理有用。
Three dimensional confocal scanning laser microscope images offer dramatic visualizations of the action 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, 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.