TY - JOUR
T1 - A full row-rank system matrix generated along two directions in discrete tomography
AU - Li, Xiezhang
AU - Wang, Hua
AU - Wu, Yan
AU - Zhu, Jiehua
PY - 2011/9/1
Y1 - 2011/9/1
N2 - A full row-rank system matrix generated by the strip-based projection model along one scanning direction was studied recently in [9]. 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.
AB - A full row-rank system matrix generated by the strip-based projection model along one scanning direction was studied recently in [9]. 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.
KW - Full row-rank system
KW - Minimal linearly dependent set
KW - Strip-based projection
UR - http://www.scopus.com/inward/record.url?scp=79959720636&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2011.05.058
DO - 10.1016/j.amc.2011.05.058
M3 - Article
SN - 0096-3003
VL - 218
SP - 107
EP - 114
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
IS - 1
ER -