ON RANDOM TOMOGRAPHY WITH UNOBSERVABLE PROJECTION ANGLES

• 成果类型: Article
• 署名作者: Panaretos, Victor M.
• 署名单位: Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/08-AOS673
• 发表日期: 2009
• 页码: 3272-3306
• 关键词: positron-emission-tomography; electron crystallography; maximum-likelihood; least-squares; diffusion; distances

摘要

We formulate and investigate a statistical inverse problem of a random tomographic nature, where a probability density function on R-3 is to be recovered from observation of finitely many of its two-dimensional projections in random and unobservable directions. Such a problem is distinct from the classic problem of tomography where both the projections and the unit vectors normal to the projection plane are observable. The problem arises in single particle electron microscopy, a powerful method that biophysicists employ to learn the structure of biological macromolecules. Strictly speaking, the problem is unidentifiable and an appropriate reformulation is suggested hinging on ideas from Kendall's theory of shape. Within this setup, we demonstrate that a consistent Solution to the problem may be derived, without attempting to estimate the unknown angles, if the density is assumed to admit a mixture representation.