Recovery of bivariate functions from the values of its Radon transform using Laplace inversion

摘要

The problems of recovering a multivariate function f from the scaled values of its Laplace and Radon transforms are studied, and two novel methods for approximating and estimating the unknown function are proposed. Moreover, using the empirical counterparts of the Laplace transform of the underlying function, a new estimate of the Radon transform itself is obtained. Under smoothed conditions on the underlying function the uniform convergence of the proposed constructions are established, and their accuracy is illustrated graphically with several simple examples. (C) 2021 Elsevier B.V. All rights reserved.