ArticleMedical physics2021
Invertibility of multi-energy X-ray transform.
Article in Medical physics, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 1 paper.
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1 citing paper in PubMed.
- Invertibility of multi-energy X-ray transform.Medical physics · 2021Article
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3 authors.
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Abstract
purposeThe goal is to provide a sufficient condition for the invertibility of a multi-energy (ME) X-ray transform. The energy-dependent X-ray attenuation profiles can be represented by a set of coefficients using the Alvarez-Macovski (AM) method. An ME X-ray transform is a mapping from
methodsWe apply a general invertibility theorem to prove the equivalence of global and local invertibility for an ME X-ray transform. We explore the global invertibility through testing whether the Jacobian of the mapping
resultsThe factor related to the basis functions is always negative when the photoelectric/Compton/Rayleigh basis functions are used and K-edge materials are not considered. The sign of the energy-weighting factor depends on the system source spectra and the detector response functions. For four special types of X-ray detectors, the sign of this factor stays the same over the integration range. Therefore, when these four types of detectors are used for imaging non-K-edge materials, the ME X-ray transform is globally invertible. The same framework can be used to study an arbitrary ME X-ray imaging system, for example, when K-edge materials are present. Furthermore, the ML estimator we presented is an unbiased, efficient estimator and can be used for a wide range of scenes.
conclusionsWe have provided a framework to study the invertibility of an arbitrary ME X-ray transform and proved the global invertibility for four types of systems.
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