Graph Laplacian tomography from unknown random projections

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.