M. Ceko ; L. Hajdu ; R. Tijdeman - Error Correction for Discrete Tomography

fi:11201 - Fundamenta Informaticae, September 21, 2023, Volume 189, Issue 2: Tomography and Applications 2022
Error Correction for Discrete TomographyArticle

Authors: M. Ceko ; L. Hajdu ; R. Tijdeman

    Discrete tomography focuses on the reconstruction of functions $f: A \to \mathbb{R}$ from their line sums in a finite number $d$ of directions, where $A$ is a finite subset of $\mathbb{Z}^2$. Consequently, the techniques of discrete tomography often find application in areas where only a small number of projections are available. In 1978 M.B. Katz gave a necessary and sufficient condition for the uniqueness of the solution. Since then, several reconstruction methods have been introduced. Recently Pagani and Tijdeman developed a fast method to reconstruct $f$ if it is uniquely determined. Subsequently Ceko, Pagani and Tijdeman extended the method to the reconstruction of a function with the same line sums of $f$ in the general case. Up to here we assumed that the line sums are exact. In this paper we investigate the case where a small number of line sums are incorrect as may happen when discrete tomography is applied for data storage or transmission. We show how less than $d/2$ errors can be corrected and that this bound is the best possible.

    Volume: Volume 189, Issue 2: Tomography and Applications 2022
    Published on: September 21, 2023
    Accepted on: July 10, 2023
    Submitted on: April 17, 2023
    Keywords: Mathematics - Combinatorics

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