期刊
ANNALS OF STATISTICS
卷 37, 期 6A, 页码 3272-3306出版社
INST MATHEMATICAL STATISTICS
DOI: 10.1214/08-AOS673
关键词
Deconvolution; mixture density; modular inference; Radon transform; shape theory; single particle electron microscopy; statistical inverse problem; trigonometric moment problem
资金
- NSF
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.
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