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November  2007, 1(4): 623-642. doi: 10.3934/ipi.2007.1.623

Two-Dimensional tomography with unknown view angles

Lars Lamberg 1, and  Lauri Ylinen 2,

1. 

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

Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, 00014 Helsinki, Finland

Received  January 2007 Published  October 2007

We consider uniqueness of two-dimensional parallel beam tomography with unknown view angles. We show that infinitely many projections at unknown view angles of a sufficiently asymmetric object determine the object uniquely. An explicit expression for the required asymmetry is given in terms of the object's geometric moments. We also show that under certain assumptions finitely many projections guarantee uniqueness for the unknown view angles. Compared to previous results about uniqueness of view angles, our result reduces the minimum number of required projections to approximately half and is applicable to a larger set of objects. Our analysis is based on algebraic geometric properties of a certain system of homogeneous polynomials determined by the Helgason-Ludwig consistency conditions.
Keywords: Uniqueness, Resultant., Homogeneous system, Geometric moment, Bezout's theorem, Unknown view angle, Radon transform, Tomography, Projective space.
Mathematics Subject Classification: Primary: 65R32, 44A1.
Citation: Lars Lamberg, Lauri Ylinen. Two-Dimensional tomography with unknown view angles. Inverse Problems and Imaging, 2007, 1 (4) : 623-642. doi: 10.3934/ipi.2007.1.623
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