Nonstationary and Nonlinear Sinogram Filtering for Tomographic Image Reconstruction

Thesis or Dissertation


There are numerous methods for implementing tomographic imagereconstruction. Commercially, the technique which is most commonlyused is filtered backprojection (FBP), due to its simplicityin computation. However, this technique is not the most appropriatein cases where the data set is incomplete or the signal-to-noise ratiois low. Therefore, methods based on statistics have been introduced,such as maximum a posteriori (MAP) estimation. These methods rely onmodeling the process of projection data generation and modeling of theimage a priori. Since the reconstruction problem posed in thismanner usually reduces to an optimization problem, a variety of iterativenumerical methods for solving this problem has been explored.This dissertation will explore techniques for tomographic imagereconstruction that use non-standard two-dimensional filtering of thesinogram prior to conventional backprojection. These techniques take advantageof features of both the conventional and statistical methods. In the firstof our techniques, we will developoptimal nonstationary linear sinogram filters based on sinogramstatistics. The advantages of this method are the exploitation ofcorrelation information among the projections of the sinogram data forthe filter design, while maintaining a low computational cost for thereconstruction, comparable to that of FBP.

This document also introduces a second technique named nonlinearbackprojection (NBP), which attempts to directly model thepseudo-optimal reconstruction operator through off-line training.This allows a more general, less explicit modeling of the data thanthe traditional statistical methods. The reconstruction of the imageis non-iterative, reducing the cost of the method but achievingquality comparable to that of other statistical methods. Results withboth methods introduced in this dissertation refute the commonly heldbelief that sinogram filtering should be one-dimensional alongthe radial variable.


Attribute NameValues
  • etd-06132003-154222

Author Blanca Isabel Andia
Advisor Dr. Andre Palmer
Contributor Dr. Peter Bauer, Committee Member
Contributor Dr. Ken Sauer, Committee Member
Contributor Dr. Yih-Fang Huang, Committee Member
Contributor Dr. Robert Stevenson, Committee Member
Contributor Dr. Andre Palmer, Committee Chair
Degree Level 2
Degree Discipline Electrical Engineering
Degree Name Doctor of Philosophy
Defense Date
  • 2003-06-09

Submission Date 2003-06-13
  • United States of America

  • sinogram filtering

  • image reconstruction

  • tomography

  • University of Notre Dame

  • English

Access Rights Open Access
Content License
  • All rights reserved