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• W2948103689 abstract "The problem of image reconstruction is to produce an image of a distribution that is compatible with constraints provided by measurements of its line integrals (i. e., values of its Radon transform) along a finite number of lines of known locations and with other possible constraints, such as nonnegativity. Algebraic reconstruction techniques (ART) form a family of iterative algorithms used for image reconstruction. Their distinguishing features are: (1) they assume that the image is represented as a linear combination of some known basis functions and (2) the unknown coefficients in this linear combination are estimated by an iterative process in which just one of the measured line integrals is used in any one iterative step. The first section of the chapter gives a tutorial overview of variants of ART, concentrating on the mathematical results regarding them and mentioning their computational efficiency in various applications. All variants of ART aim at producing an image that is compatible with the constraints, such constraints-compatibility is mathematically defined by what is referred to as the primary criterion. The second section of the chapter is devoted to the superiorization methodology, which is a recently-developed heuristic approach to optimization, and to a discussion of its applicability to improving the results of iterative approaches to inverting the Radon transform. The underlying idea is that many iterative algorithms for finding such an inverse are perturbation resilient in the sense that, even if certain kinds of changes are made at the end of each iterative step, the algorithm still produces a constraints-compatible solution. This property is exploited by using permitted changes to steer the algorithm to a solution that is not only constraints-compatible, but is also desirable according to a specified secondary criterion. The approach is very general, it is applicable to many iterative procedures and secondary criteria used in the inversion of the Radon transform. Superiorization produces automatically from any given iterative algorithm its superiorized version. If the original iterative algorithm satisfies certain mathematical conditions, then the output of its superiorized version is guaranteed to be as good as the output of the original algorithm from the point of view of the primary criterion, but it is superior to the latter according to the secondary criterion. This intuitive description is made more precise and is illustrated in the second section of the chapter." @default.
• W2948103689 created "2019-06-14" @default.
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• W2948103689 date "2019-06-17" @default.
• W2948103689 modified "2023-09-25" @default.
• W2948103689 title "10. Iterative reconstruction techniques and their superiorization for the inversion of the Radon transform" @default.
• W2948103689 doi "https://doi.org/10.1515/9783110560855-010" @default.
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