Term of Award

Spring 2010

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (restricted to Georgia Southern)

Department

Department of Mathematical Sciences

Committee Chair

Xiezhang Li

Committee Member 1

Jiehua Zhu

Committee Member 2

Yan Wu

Committee Member 3

n/a

Abstract

We propose and study the reconstruction of large binary images in discrete tomography (DT) by applying the binary steering scheme to the block-iterative projections methods for solving an underdetermined linear system Ax = b. Three algorithms: Algebraic Reconstruction Technique (ART) Algorithm, Cimmino's Algorithm (CIM) with Equal Weights Algorithm and Fully-Simultaneous Diagonally-Relaxed Orthogonal Projections (DROP) Algorithm are modified. We develop an efficient storage of the binary sparse system matrix A and analyze the work load of the fast execution of the matrix-vector multiplication Ax. Numerical experiments are given to illustrate faster convergence by binary steering block iterations and efficient storage of A.

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