Construction of a full row-rank matrix system for multiple scanning directions in discrete tomography
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- 作者：Xiezhang Lia ; xli@georgiasouthern.edu" class="auth_mail" title="E-mail the corresponding author ; James Diffenderferb ; Jiehua Zhua
- 关键词：Strip-based projection model ; Full row-rank system ; Minimal linearly dependent
- 刊名：Journal of Computational and Applied Mathematics
- 出版年：2017
- 出版时间：February 2017
- 年：2017
- 卷：311
- 期：Complete
- 页码：529-538
- 全文大小：1001 K
文摘
A full row-rank system matrix generated by scans along two directions in discrete tomography was recently studied. In this paper, we generalize the result to multiple directions. Let 
be a reduced binary linear system generated by scans along three directions. Using geometry, it is shown in this paper that the linearly dependent rows of the system matrix A can be explicitly identified and a full row-rank matrix can be obtained after the removal of those rows. The results could be extended to any number of multiple directions. Therefore, certain software packages requiring a full row-rank system matrix can be adopted to reconstruct an image. Meanwhile, the cost of computation is reduced by using a full row-rank matrix.
be a reduced binary linear system generated by scans along three directions. Using geometry, it is shown in this paper that the linearly dependent rows of the system matrix A can be explicitly identified and a full row-rank matrix can be obtained after the removal of those rows. The results could be extended to any number of multiple directions. Therefore, certain software packages requiring a full row-rank system matrix can be adopted to reconstruct an image. Meanwhile, the cost of computation is reduced by using a full row-rank matrix.