Hierarchical Reconstruction Using Geometry and Sinogram Restoration
JOHNS HOPKINS UNIV BALTIMORE MD DEPT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE
Pagination or Media Count:
We describe and demonstrate a hierarchical reconstruction algorithm for use in noisy and limited-angle or sparse-angle tomography. The algorithm estimates an objects 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.
- Statistics and Probability