• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1773-1781
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• 2018

The Radon transform introduced by J. Radon in 1917 is the integral transform which is widely applicable to tomography. Here we study the discrete version of the Radon transform. More precisely, when $C({\mathbb{Z}}^n_p)$ is the set of complex-valued functions on ${\mathbb{Z}}^n_p$. We completely determine the subset of $C({\mathbb{Z}}^n_p)$ whose elements can be recovered from its Radon transform on ${\mathbb{Z}}^n_p$.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.21 no.1
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• pp.29-37
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• 2017

A general optimal recovery problem is to approximate a value of a linear operator on a subset (class) in linear space from a value of another linear operator (called information), measured with an error in given metric. We use this formulation to investigate the classical computerized tomography problem of inversion of the noisy Radon transform.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.717-730
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• 2002

In this paper we use measure theory to solve a wide range of the nonlinear programming problems. First, we transform a nonlinear programming problem to a classical optimal control problem with no restriction on states and controls. The new problem is modified into one consisting of the minimization of a special linear functional over a set of Radon measures; then we obtain an optimal measure corresponding to functional problem which is then approximated by a finite combination of atomic measures and the problem converted approximately to a finite-dimensional linear programming. Then by the solution of the linear programming problem we obtain the approximate optimal control and then, by the solution of the latter problem we obtain an approximate solution for the original problem. Furthermore, we obtain the path from the initial point to the admissible solution.