AN ALGEBRAIC FRAMEWORK FOR DISCRETE TOMOGRAPHY: REVEALING THE STRUCTURE OF DEPENDENCIES

作者：Stolk Arjen^*; Batenburg K Joost

来源：SIAM Journal on Discrete Mathematics, 2010, 24(3): 1056-1079.

DOI：10.1137/090766693

• discrete tomography
• reconstruction of integer-valued functions
• dependencies between line sums

Discrete tomography is concerned with the reconstruction of images that are defined on a discrete set of lattice points from their projections in several directions. The range of values that can be assigned to each lattice point is typically a small discrete set. In this paper we present a framework for studying these problems from an algebraic perspective, based on ring theory and commutative algebra. A principal advantage of this abstract setting is that a vast body of existing theory becomes accessible for solving discrete tomography problems. We provide proofs of several new results on the structure of dependencies between projections, including a discrete analogon of the well-known Helgason Ludwig consistency conditions from continuous tomography.

• 出版日期2010