An inversion formula for the attenuated X-ray transformation

By R. Novikov. 2002

309 citations recorded by the source corpus.

Subfields: Condensed Matter Physics, Radiation, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/5da25351c70d7db686b3682294dc60d0d9de1e35

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In Condensed Matter Physics

In Radiation

In Radiology, Nuclear Medicine and Imaging

Citations in the corpus

Novikov’s inversion formula for the attenuated Radon transform—A new approach (2004, methodology): “In [5] Novikov also proved injectivity for the attenuated Radon transform with the angle variable θ restricted to an arbitrarily small open set.”
Reconstructive Integral Geometry (2004, methodology): “This property is exploited in the efficient algorithms [63] which give the same accuracy as the standard reconstruction.”
Explicit inversion formulae for the spherical mean Radon transform (2006, background): “It is worth noting that such a divergence form of a reconstruction formula is not unusual; it also naturally occurs in reconstruction formulae for the attenuated Radon transform (see, for instance [20]).”
ON DETERMINATION OF A GAUGE FIELD ON ℝd FROM ITS NON-ABELIAN RADON TRANSFORM ALONG ORIENTED STRAIGHT LINES (2002, methodology): “5), well-known results for the two-dimensional transformation P and the explicit inversion formula of [15] for the twodimensional transformation Pμ imply that the non-abelian Radon transform S uniquely determines a0.”
The attenuated ray transform on simple surfaces (2010, methodology): “It seems that even when M is a domain in R2 with Euclidean metric, the reconstruction procedure does not reduce to a simple formula such as in [12], [22].”
Inverse transport theory and applications (2009, background): “Under mild regularity assumptions on σ , the attenuated Radon transform was shown in [5, 104] to be injective and in [104] (see also [33]) to admit an explicit inversion formula.”