A Full Row-Rank System Matrix Generated Along Two Directions in Discrete Tomography
Applied Mathematics and Computation
A full row-rank system matrix generated by the strip-based projection model along one scanning direction was studied recently in . In this paper, we generalize the result to multiple directions. Let Cu = h be a reduced binary linear system generated along two distinct scanning directions by the strip-based projection model in discrete tomography, where C is row-rank deficient. We identify all the linearly dependent rows explicitly through a partition of the rows of C into minimal linearly dependent sets. The removal of these linearly dependent rows results in a full-rank matrix. Consequently, the computational cost for image reconstruction is reduced.
Li, Xiezhang, Hua Wang, Yan Wu, Jiehua Zhu.
"A Full Row-Rank System Matrix Generated Along Two Directions in Discrete Tomography."
Applied Mathematics and Computation, 218 (1): 107-114.