标题： 随机场的低剂量断层扫描与连续非均质性问题 显示英文标题

标题： Low-Dose Tomography of Random Fields and the Problem of Continuous Heterogeneity

摘要： 我们考虑基于低剂量断层扫描的代表性个体随机样本，对相关结构群体中的构象变异进行非参数估计的问题。 在此背景下，每个个体代表一个共同模板的随机扰动，并且仅在少数投影角度上被噪声和离散地成像。 这类问题出现在结构异质生物大分子的冷冻电子显微镜中。 我们将种群建模为一个随机场，其均值捕捉典型结构，其协方差反映异质性。 我们证明即使每个个体仅有两个投影，也可以实现一致估计，并推导出反映问题各种参数如何影响统计效率及其权衡的统一收敛速率。 我们的分析将正向算子的定义域设定为再生核希尔伯特空间，在其中建立了针对当前问题量身定制的表示定理和Mercer定理。 这使我们能够利用功能数据分析中核心的池化估计策略，并在新颖的背景下展示了它们的灵活性。 我们使用张量化的Krylov方法提供了高效的计算实现，并通过模拟演示了我们方法的性能。 显示英文摘要

摘要： We consider the problem of nonparametric estimation of the conformational variability in a population of related structures, based on low-dose tomography of a random sample of representative individuals. In this context, each individual represents a random perturbation of a common template and is imaged noisily and discretely at but a few projection angles. Such problems arise in the cryo Electron Microscopy of structurally heterogeneous biological macromolecules. We model the population as a random field, whose mean captures the typical structure, and whose covariance reflects the heterogeneity. We show that consistent estimation is achievable with as few as two projections per individual, and derive uniform convergence rates reflecting how the various parameters of the problem affect statistical efficiency, and their trade-offs. Our analysis formulates the domain of the forward operator to be a reproducing kernel Hilbert space, where we establish representer and Mercer theorems tailored to question at hand. This allows us to exploit pooling estimation strategies central to functional data analysis, illustrating their versatility in a novel context. We provide an efficient computational implementation using tensorized Krylov methods and demonstrate the performance of our methodology by way of simulation.