An algorithm for recovering unknown projection orientations and shifts in 3-D tomography

Jaakko Ketola; Lars Lamberg

doi:10.3934/ipi.2011.5.75

Article Contents

2011, Volume 5, Issue 1: 75-93. Doi: 10.3934/ipi.2011.5.75

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An algorithm for recovering unknown projection orientations and shifts in 3-D tomography

Jaakko Ketola^1, and
Lars Lamberg^2,

1.
Department of Mathematics and Physics, Lappeenranta University of Technology, Lappeenranta
2.
Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, 00014 Helsinki,

Received: February 28, 2010

Revised: June 30, 2010

Published: January 2011

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Abstract

It is common for example in Cryo-electron microscopy of viruses, that the orientations at which the projections are acquired, are totally unknown. We introduce here a moment based algorithm for recovering them in the three-dimensional parallel beam tomography. In this context, there is likely to be also unknown shifts in the projections. They will be estimated simultaneously. Also stability properties of the algorithm are examined. Our considerations rely on recent results that guarantee a solution to be almost always unique. A similar analysis can also be done in the two-dimensional problem.

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Mathematics Subject Classification: Primary: 65R32, 44A12.

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