## Three-dimensional reconstruction of the statistics of heterogeneous objects from a collection of one projection image of each object |

JOSA A, Vol. 29, Issue 6, pp. 959-970 (2012)

http://dx.doi.org/10.1364/JOSAA.29.000959

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### Abstract

An estimation problem for statistical reconstruction of heterogeneous three-dimensional objects from two-dimensional tomographic data (single-particle cryoelectron microscope images) is posed as the problem of estimating class probabilities, means, and covariances for a Gaussian mixture where both the mean and covariance are stochastically structured. Both discrete (i.e., classes) and continuous heterogeneity is included. A maximum likelihood solution computed by a generalized expectation-maximization algorithm is presented and demonstrated on experimental images of Flock House Virus.

© 2012 Optical Society of America

**OCIS Codes**

(100.3010) Image processing : Image reconstruction techniques

(100.3190) Image processing : Inverse problems

(100.6890) Image processing : Three-dimensional image processing

(100.6950) Image processing : Tomographic image processing

(170.3880) Medical optics and biotechnology : Medical and biological imaging

**ToC Category:**

Image Processing

**History**

Original Manuscript: August 30, 2011

Manuscript Accepted: December 9, 2011

Published: May 23, 2012

**Virtual Issues**

Vol. 7, Iss. 8 *Virtual Journal for Biomedical Optics*

**Citation**

Yili Zheng, Qiu Wang, and Peter C. Doerschuk, "Three-dimensional reconstruction of the statistics of heterogeneous objects from a collection of one projection image of each object," J. Opt. Soc. Am. A **29**, 959-970 (2012)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=josaa-29-6-959

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