TY - JOUR
T1 - Algorithms for linear time reconstruction by discrete tomography
AU - Pagani, Silvia Maria Carla
AU - Tijdeman, Rob
PY - 2019
Y1 - 2019
N2 - We present an algorithm that for any given rectangular grid A∈Z2 and set of directions D computes in linear time the values of any function f:A→R outside the convex hull of the union of the switching domains from its line sums in the directions of D. Moreover, the algorithm reconstructs f completely if there are no switching domains. We present a simpler algorithm in case the directions satisfy some monotonicity condition. Finally, for given A we propose how to choose the set D so that only a small number of directions is needed to reconstruct any f from its line sums in the directions of D.
AB - We present an algorithm that for any given rectangular grid A∈Z2 and set of directions D computes in linear time the values of any function f:A→R outside the convex hull of the union of the switching domains from its line sums in the directions of D. Moreover, the algorithm reconstructs f completely if there are no switching domains. We present a simpler algorithm in case the directions satisfy some monotonicity condition. Finally, for given A we propose how to choose the set D so that only a small number of directions is needed to reconstruct any f from its line sums in the directions of D.
KW - Discrete tomography
KW - Lattice direction
KW - Reconstruction algorithm
KW - Region of uniqueness
KW - Discrete tomography
KW - Lattice direction
KW - Reconstruction algorithm
KW - Region of uniqueness
UR - http://hdl.handle.net/10807/144434
UR - https://www.journals.elsevier.com/discrete-applied-mathematics
U2 - 10.1016/j.dam.2019.07.012
DO - 10.1016/j.dam.2019.07.012
M3 - Article
SN - 0166-218X
VL - 271
SP - 152
EP - 170
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
ER -