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Type of Document Dissertation Author Andia, Blanca Isabel Author's Email Address Blanca.Andia.1@nd.edu URN etd-06132003-154222 Title Nonstationary and Nonlinear Sinogram Filtering for Tomographic Image Reconstruction Degree Doctor of Philosophy Department Electrical Engineering Advisory Committee
Advisor Name Title Dr. Andre Palmer Committee Chair Dr. Ken Sauer Committee Member Dr. Peter Bauer Committee Member Dr. Robert Stevenson Committee Member Dr. Yih-Fang Huang Committee Member Keywords
- image reconstruction
- sinogram filtering
- tomography
Date of Defense 2003-06-09 Availability unrestricted Abstract There are numerous methods for implementing tomographic imagereconstruction. Commercially, the technique which is most commonly
used is filtered backprojection (FBP), due to its simplicity
in computation. However, this technique is not the most appropriate
in cases where the data set is incomplete or the signal-to-noise ratio
is low. Therefore, methods based on statistics have been introduced,
such as maximum a posteriori (MAP) estimation. These methods rely on
modeling the process of projection data generation and modeling of the
image a priori. Since the reconstruction problem posed in this
manner usually reduces to an optimization problem, a variety of iterative
numerical methods for solving this problem has been explored.
This dissertation will explore techniques for tomographic image
reconstruction that use non-standard two-dimensional filtering of the
sinogram prior to conventional backprojection. These techniques take advantage
of features of both the conventional and statistical methods. In the first
of our techniques, we will develop
optimal nonstationary linear sinogram filters based on sinogram
statistics. The advantages of this method are the exploitation of
correlation information among the projections of the sinogram data for
the filter design, while maintaining a low computational cost for the
reconstruction, comparable to that of FBP.
This document also introduces a second technique named nonlinear
backprojection (NBP), which attempts to directly model the
pseudo-optimal reconstruction operator through off-line training.
This allows a more general, less explicit modeling of the data than
the traditional statistical methods. The reconstruction of the image
is non-iterative, reducing the cost of the method but achieving
quality comparable to that of other statistical methods. Results with
both methods introduced in this dissertation refute the commonly held
belief that sinogram filtering should be one-dimensional along
the radial variable.
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