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IEEE Trans Image Process. 2008 Oct;17(10):1891-9. doi: 10.1109/TIP.2008.2002305.

Graph Laplacian tomography from unknown random projections.

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  • 1Department of Mathematics, Program in Applied Mathematics, Yale University, New Haven, CT 06520-8283, USA.


We introduce a graph Laplacian-based algorithm for the tomographic reconstruction of a planar object from its projections taken at random unknown directions. A Laplace-type operator is constructed on the data set of projections, and the eigenvectors of this operator reveal the projection orientations. The algorithm is shown to successfully reconstruct the Shepp-Logan phantom from its noisy projections. Such a reconstruction algorithm is desirable for the structuring of certain biological proteins using cryo-electron microscopy.

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