Explicit inversion formulas for the \(X\)-ray transform in \(\mathbb{Z}^n\)
The author reconstructs a function \(f\) defined on the lattice \({\mathbb{Z}^n}\) with finite support from its \(d\)-plane Radon transform. He establishes also a Plancherel formula relatively at discrete Radon transform for the functions \(f\) on \({\mathbb{Z}^n}\). Finally, the author states and proves explicit inversion formulas for the \(X\)-ray transform in the lattice \({\mathbb{Z}^n}\) by using certain arithmetical geometrical techniques. Also, another inversion formula for the discrete \(d\)-plane Radon transform is given.
scientific article; zbMATH DE number 5841053