Two-Dimensional Tomography from Noisy Projections Taken at Unknown Random Directions.


Journal Article

Computerized tomography is a standard method for obtaining internal structure of objects from their projection images. While CT reconstruction requires the knowledge of the imaging directions, there are some situations in which the imaging directions are unknown, for example, when imaging a moving object. It is therefore desirable to design a reconstruction method from projection images taken at unknown directions. Another difficulty arises from the fact that the projections are often contaminated by noise, practically limiting all current methods, including the recently proposed diffusion map approach. In this paper, we introduce two denoising steps that allow reconstructions at much lower signal-to-noise ratios (SNRs) when combined with the diffusion map framework. In the first denoising step we use principal component analysis (PCA) together with classical Wiener filtering to derive an asymptotically optimal linear filter. In the second step, we denoise the graph of similarities between the filtered projections using a network analysis measure such as the Jaccard index. Using this combination of PCA, Wiener filtering, graph denoising, and diffusion maps, we are able to reconstruct the two-dimensional (2-D) Shepp-Logan phantom from simulative noisy projections at SNRs well below their currently reported threshold values. We also report the results of a numerical experiment corresponding to an abdominal CT. Although the focus of this paper is the 2-D CT reconstruction problem, we believe that the combination of PCA, Wiener filtering, graph denoising, and diffusion maps is potentially useful in other signal processing and image analysis applications.

Full Text

Duke Authors

Cited Authors

  • Singer, A; Wu, H-T

Published Date

  • January 2013

Published In

Volume / Issue

  • 6 / 1

Start / End Page

  • 136 - 175

PubMed ID

  • 24563691

Pubmed Central ID

  • 24563691

Electronic International Standard Serial Number (EISSN)

  • 1936-4954

International Standard Serial Number (ISSN)

  • 1936-4954

Digital Object Identifier (DOI)

  • 10.1137/090764657


  • eng