2D vector tomography with broken rays and stars

Abstract: Multiple classical works of integral geometry have been dedicated to the reconstruction of vector fields from various integral transforms of such fields, including the longitudinal ray transform (Doppler transform), transverse ray transform, and their integral moments. We consider a generalization of these transforms, in which the straight-line path of integration is substituted either by broken rays or by stars (a finite union of rays emanating from a common vertex). We present several exact closed-form inversion formulas for certain pairs of these transforms on 2D compactly supported vector fields in the plane, discuss their properties and present results of numerical simulations. The talk is based on joint work with Mohammad Latifi (University of Arizona) and Rohit Mishra (University of Texas at Arlington).

Mathematics

Audience: researchers in the topic

International Zoom Inverse Problems Seminar, UC Irvine