Graph Laplacian tomography from unknown random projections

Ronald R. Coifman, Yoel Shkolnisky, Fred J. Sigworth, Amit Singer

Research output: Contribution to journalArticlepeer-review

141 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1891-1899
Number of pages9
JournalIEEE Transactions on Image Processing
Issue number10
StatePublished - 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Graphics and Computer-Aided Design


  • Dimensionality reduction
  • Graph laplacian
  • Tomography


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