Graph Laplacian Tomography From Unknown Random Projections

Authors:
R. R. Coifman;Y. Shkolnisky;F. J. Sigworth;A. Singer
Affiliations:
Dept. of Math., Yale Univ., New Haven, CT;-;-;-
Venue:
IEEE Transactions on Image Processing
Year:
2008

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Abstract

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.