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.
","abstract_html":"<p>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.</p>","abstract_has_math":false,"creators":["Seetong, Wandee"],"institution":null,"degree_name":"Master of Science in Mathematics (M.S.)","degree_level":"Thesis (restricted to Georgia Southern)","degree_discipline":"Department of Mathematical Sciences","degree_department":null,"school":null,"contributors":["Jiehua Zhu","Yan Wu","n/a"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-01-01T08:00:00Z","date_published":"2010-01-01T08:00:00Z","updated_at":"2026-07-24T02:27:19Z","subjects":["ETD","Discrete tomography","Binary steering","Block-iterative reconstruction algorithms","Sparse matrix","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/683","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Jiehua Zhu","Yan Wu","n/a"]},{"key":"dc:creator","label":"Author","values":["Seetong, Wandee"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2013-08-07T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis (restricted to Georgia Southern)"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Mathematics (M.S.)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["ETD","Discrete tomography","Binary steering","Block-iterative reconstruction algorithms","Sparse matrix","Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.georgiasouthern.edu/etd/683"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["The Reconstruction of Binary Images in Discrete Tomography by Using the Binary Steering Scheme"]}]}],"canonical_facts":{"dc:contributor":["Jiehua Zhu","Yan Wu","n/a"],"dc:creator":["Seetong, Wandee"],"dc:date.available":["2013-08-07T07:00:00Z"],"dc:description.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.
"],"dc:identifier":["https://digitalcommons.georgiasouthern.edu/etd/683"],"dc:subject":["ETD","Discrete tomography","Binary steering","Block-iterative reconstruction algorithms","Sparse matrix","Mathematics"],"dc:title":["The Reconstruction of Binary Images in Discrete Tomography by Using the Binary Steering Scheme"],"thesis:degree_discipline":["Department of Mathematical Sciences"],"thesis:degree_level":["Thesis (restricted to Georgia Southern)"],"thesis:degree_name":["Master of Science in Mathematics (M.S.)"]},"updated_at":"2026-07-24T02:27:19Z"}