Abstract
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.
Lingua originale | English |
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pagine (da-a) | 152-170 |
Numero di pagine | 19 |
Rivista | Discrete Applied Mathematics |
Volume | 271 |
DOI | |
Stato di pubblicazione | Pubblicato - 2019 |
Keywords
- Discrete tomography
- Lattice direction
- Reconstruction algorithm
- Region of uniqueness