Showing papers by "Eric Todd Quinto published in 1993"
TL;DR: In this paper, the authors specify the singularities of a function f that are visible in a stable way from limited X-ray tomographic data and determine which singularities can be stably recovere...
Abstract: Given a function f, the author specifies the singularities of f that are visible in a stable way from limited X-ray tomographic data. This determines which singularities of f can be stably recovere...
308 citations
TL;DR: Support theorems for Radon transforms with arbitrary nonzero real analytic measures on line complexes (three-dimensional sets of lines) in R 3 have been proved in this article, using analytic microlocal analysis and information about the analytic wave front set of a distribution at the boundary of its support.
Abstract: In this article we prove support theorems for Radon transforms with arbitrary nonzero real analytic measures on line complexes (three-dimensional sets of lines) in R 3 . Let f be a distribution of compact support on R 3 . Assume Y is a real analytic admissible line complex and Y 0 is an open connected subset of Y with one line in Y 0 disjoint from supp f. Under weak geometric assumptions, if the Radon transform of f is zero for all lines in Y 0 , then supp f intersects no line in Y 0 . These theorems are more general than previous results, even for the classical transform. We also prove a support theorem for the Radon transform on a nonadmissible line complex. Our proofs use analytic microlocal analysis and information about the analytic wave front set of a distribution at the boundary of its support
41 citations
TL;DR: In this paper, a support theorem for the Pompeiu transform integrating on geodesic spheres of fixed radius r>0 on real analytic manifolds was proved, where r is the injectivity radius at the center of each sphere being integrated over.
Abstract: We prove a support theorem for Pompeiu transforms integrating on geodesic spheres of fixed radiusr>0 on real analytic manifolds when the measures are real analytic and nowhere zero. To avoid pathologies, we assume thatr is less than the injectivity radius at the center of each sphere being integrated over. The proof of the main result is local and it involves the microlocal properties of the Pompeiu transform and a theorem of Hormander, Kawai, and Kashiwara on microlocal singularities.
28 citations
01 Jan 1993
TL;DR: In this article, the authors proved support theorems for Radon transforms with real analytic measures on horocycles in rank one symmetric spaces using microlocal techniques, and generalized Helgason's support theorem to this case and proved a new local support theorem.
Abstract: Using microlocal techniques, we prove support theorems for Radon transforms with real analytic measures on horocycles in rank one symmetric spaces. We generalize Helgason's support theorem to this case and prove a new local support theorem
17 citations