A Bayesian Approach to Reconstruction from Incomplete Projections of a Multiple Object 3D Domain

Yoram Bresler, Jeffrey A. Fessler, Albert Macovski

Research output: Contribution to journalArticlepeer-review


An estimation approach is described for three-dimensional reconstruction from line integral projections using incomplete and very noisy data. Generalized cylinders parameterized by stochastic dynamic models are used to represent prior knowledge about the properties of objects of interest in the probed domain. The object models, a statistical measurement model, and the maximum a posteriori probability performance criterion are combined to reformulate the reconstruction problem as a computationally challenging nonlinear estimation problem. For computational feasibility, a suboptimal hierarchical algorithm is described whose individual steps are locally optimal and are combined to satisfy a global optimality criterion. The formulation and algorithm are restricted to objects whose center axis is a single-valued function of a fixed spatial coordinate. Simulation examples demonstrate accurate reconstructions with as few as four views in a 135° sector, at an average signal-to-noise ratio of 3.3.

Original languageEnglish (US)
Pages (from-to)840-858
Number of pages19
JournalIEEE transactions on pattern analysis and machine intelligence
Issue number8
StatePublished - Aug 1989


  • Hierarchical algorithm
  • nonlinear estimation and detection
  • parametric inference
  • stochastic object modeling
  • three-dimension tomography with incomplete data

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics


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