Reconstruction from limited data of arc means
Let \(f\) be a function in a Euclidean plane with compact support in a half disk \(H\). The local arc problem, i.e. the problem of reconstruction of \(f\) from the data of its integrals over half circles \(A \subset H\) with centers at the diameter of \(H\) is studied: Reduction of the local arc problem to the limited angle problem for the Euclidean Radon transform. Explicit formulae for the reconstruction. Plancherel-type identity that equalizes a weighted \(L_2\)-norm of the original \(f\) with a Sobolev-type norm of its arc mean transform \(Mf\). Microlocal analysis of stability of the reconstruction.
scientific article; zbMATH DE number 1445624
scientific article