# American Institute of Mathematical Sciences

February  2011, 5(1): 75-93. doi: 10.3934/ipi.2011.5.75

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

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

Received  March 2010 Revised  July 2010 Published  February 2011

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.
Citation: Jaakko Ketola, Lars Lamberg. An algorithm for recovering unknown projection orientations and shifts in 3-D tomography. Inverse Problems & Imaging, 2011, 5 (1) : 75-93. doi: 10.3934/ipi.2011.5.75
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