Term of Award

Summer 2016

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (open access)

Department

Department of Mathematical Sciences

Committee Chair

Jiehua Zhu

Committee Member 1

Xiezhang Li

Committee Member 2

Yan Wu

Abstract

Discrete tomography (DT) is an image reconstruction procedure that deals with computational synthesis of a cross-sectional image of an object from either transmission or reflection data collected by penetrating an object with X-rays from a small number of different directions, and whose range of the underlying function is discrete. Image reconstruction using algebraic approach is time consuming and the computation cost depends on the size of the system matrix. More scanning directions provide an increase in the reconstructed image quality, however they increase the size of the system matrix dramatically. Deletion of linearly dependent rows of this matrix is necessary to reduce computational cost, and is sometimes a requirement for certain reconstruction software. A geometric-based algorithm is derived in this study that will remove linearly dependent rows of the system matrix generated along an arbitrary number of scanning directions. Numerical experiments indicate that the proposed algorithm reduces the system matrix to a full row-rank.

Research Data and Supplementary Material

No

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