Integral Geometry and Radon Transforms

By S. Helgason. 2010

333 citations recorded by the source corpus.

Subfields: Applied Mathematics, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/a6442377d603fcbebb164408cd96ad0639455d2f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Radiology, Nuclear Medicine and Imaging

Citations in the corpus

A stereoscopic look into the bulk (2016, background): “1 A Brief Introduction to X-ray Transforms Integral geometry supplies us with canonical maps from local functions defined on a manifold M to functions on the space of totally geodesic submanifolds of dimension k [32, 33].”
Using mixtures in econometric models: a brief review and some new results (2016, background): “It is known that in (3.6) if g is in L1(Rd ), then Rg exists for almost all (z, w) ∈ Sd−1 × R and the map g → Rg is injective on L1(Rd ); see Proposition 3.4 of Helgason (2009).”
The inverse problem for the local geodesic ray transform (2012, background): “Reconstruction procedures or inversion formulas have not been proven except in a few cases for instance for a class of symmetric spaces, see [5], and real-analytic curves [3].”
Neural Network with Unbounded Activation Functions is Universal Approximator (2015, methodology): “That is, “ p R g p u , ¨q ˚ 0 q p β q (53) where the second equality follows by the intertwining relation R∆ g p u , p q “ B 2 p R g p u , p q [17].”
Unique continuation property and Poincaré inequality for higher order fractional Laplacians with applications in inverse problems (2020, background): “quality is also true for u2Hes( ). 5. Applications to integral geometry In this section we discuss how the UCP of Riesz potentials can be used in partial data problems in integral geometry. We follow [35] for the treatment of the d-plane transform, theory of X-ray transform and Radon transform can a”