Algorithms for linear time reconstruction by discrete tomography II
M Ceko, SMC Pagani, R Tijdeman - Discrete Applied Mathematics, 2021 - Elsevier
The reconstruction of an unknown function f from its line sums is the aim of discrete
tomography. However, two main aspects prevent reconstruction from being an easy task. In
general, many solutions are allowed due to the presence of the switching functions. Even
when uniqueness conditions are available, results about the NP-hardness of reconstruction
algorithms make their implementation inefficient when the values of f are in certain sets. We
show that this is not the case when f takes values in a field or a unique factorization domain …
tomography. However, two main aspects prevent reconstruction from being an easy task. In
general, many solutions are allowed due to the presence of the switching functions. Even
when uniqueness conditions are available, results about the NP-hardness of reconstruction
algorithms make their implementation inefficient when the values of f are in certain sets. We
show that this is not the case when f takes values in a field or a unique factorization domain …
[HTML][HTML] Algorithms for linear time reconstruction by discrete tomography
SMC Pagani, R Tijdeman - Discrete Applied Mathematics, 2019 - Elsevier
We present an algorithm that for any given rectangular grid A∈ Z 2 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 …
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 …
以上显示的是最相近的搜索结果。 查看全部搜索结果