Abstract
In this paper, pseudolocal and local approaches to the tomographic reconstruction of discontinuities of an unknown functionffrom its exponential Radon transform datag(θ,p) are developed. A functionfis supposed to be piecewise-continuous and compactly supported. A pseudolocal tomography functionfd(x) is introduced and it is proved that the differencef−fdis continuous. Therefore, locations and values of jumps offcan be recovered fromfd, the computation of which is pseudolocal: for the reconstruction offdat a pointxone needs to knowg(θ,p) only for (θ,p) satisfying |Θ·x−p|≤d. Investigation of the properties offdasd→0 is given. Also a local exponential tomography functionfΛ(μ)is proposed and it is proved thatfΛ(μ)is the result of action onfof an elliptic pseudo-differential operator with the principal symbol |ξ|. Thus singsupp(fΛ(μ))=singsupp(f) and, moreover, the asymptotics offΛ(μ)(x) asx→S, the discontinuity curve off, are established. These asymptotics allow one to find values of jumps offacrossSusing local exponential tomography.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
