2008/09/15 by Plamen Stefanov, Stefanov, Plamen, Alexandru Tamasan +1
Engineering · Mathematics · Medicine · #35R30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Optical Imaging and Spectroscopy Techniques #Photoacoustic and Ultrasonic Imaging #math.AP #msc:35R30
paper · pdf · doi:10.48550/arxiv.0809.2570
arxiv created 2008/09/15 · openalex publication_date 2008/09/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We characterize the non-uniqueness in the inverse problem for the stationary transport model, in which the absorption "a" and the scattering coefficient "k" are to be recovered from the albedo operator. We show that "gauge equivalent" pairs (a,k) yield the same albedo operator, and that we can recover uniquely the class of gauge equivalent pairs. We apply this result to show unique determination of the media when the absorption "a" depends on the line of travel through each point while scattering "k" obeys a symmetry property. Previously known results concerned directional independent absorption.