Hierarchical Reconstruction Using Geometry and Sinogram Restoration

Abstract

We describe and demonstrate a hierarchical reconstruction algorithm for use in noisy and limited-angle or sparse-angle tomography. The algorithm estimates an object's mass, center of mass, and convex hull from the available projections, and uses this information, along with fundamental mathematical constraints, to estimate a full set of smoothed projections. The mass and center of mass estimates are made using a least squares estimator derived from the principles of consistency of the Radon transform. The convex hull estimate is produced by first estimating the positions of support lines of the object from each available projection and then estimating the overall convex hull using maximum likelihood techniques or maximum a posteriori techniques. Estimating the position of two support lines from a single projection is accomplished using a generalized likelihood ratio technique for estimating jumps in linear systems. We show results for simulated objects in a variety of measurement situations and for several model parameters and discuss several possible extensions to the work.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1991
Accession Number
ADA459493

Entities

People

  • Alan S. Willsky
  • Jerry L. Prince

Organizations

  • Johns Hopkins University

Tags

Communities of Interest

  • Biomedical

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Computational Fluid Dynamics
  • Computational Science
  • Convex Sets
  • Detectors
  • Diagnostic Imaging
  • Equations
  • Geometry
  • Image Processing
  • Image Reconstruction
  • Kalman Filters
  • Mathematical Filters
  • Military Research
  • Probability
  • Two Dimensional
  • X-Ray Computed Tomography

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