BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Leonid Kunyansky (University of Arizona) DTSTART:20210909T160000Z DTEND:20210909T170000Z DTSTAMP:20260423T035752Z UID:Inverse/56 DESCRIPTION:Title: Parametrix for the inverse source problem of thermoacoustic tomography wi th reduced data\nby Leonid Kunyansky (University of Arizona) as part o f International Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nW e consider the inverse source problem of thermo- and photoacoustic tomogra phy\, with data registered on an open surface partially surrounding the so urce of acoustic waves. Our goal is to find efficient non-iterative\nsolut ions to this problem.\n\nI will present two different methods:\n\n(1) A pr ocedure based on solving the exterior Dirichlet problem and computing the Radon transform of the solution. This technique works under assumption of a constant speed of sound.\n\n(2) A procedure based on modifying the time- reversed solution by two Hilbert transforms\, one in time and one in a cer tain spatial variable. This techniques works for a smooth known speed of s ound\, subject to an additional geometric condition.\n\nBoth techniques pr oduce microlocally accurate approximations to the sought initial condition . In certain geometries these methods can be implemented as fast algorithm s. Performance of these techniques will be demonstrated in numerical simul ations.\n\nJoint work with M. Eller and P. Hoskins\n LOCATION:https://researchseminars.org/talk/Inverse/56/ END:VEVENT END:VCALENDAR