Projected finite dimensional iteratively regularized Gauss–Newton method with a posteriori stopping for the ionospheric radiotomography problem

Abstract

We investigate a class of finite dimensional iteratively regularized Gauss–Newton methods for solving nonlinear irregular operator equations in a Hilbert space. The developed technique allows to investigate in a uniform style various discretization methods such as projection, quadrature and collocation schemes and to take into account available restrictions on the solution. We propose an a posteriori stopping rule for the iterative process and establish an accuracy estimate for obtained approximation. The regularized Gauss–Newton method combined with the quadrature discretization and the a posteriori iteration stopping is applied to a model ionospheric radiotomography problem. The problem is reduced to a nonlinear integral equation describing the phase shift of a sounding radio signal in dependence of the free electron concentration in the ionosphericplasma.Weestablish theunique solvability of the inverse problem in the class of analytic functions. ARTICLE HISTORY Received 19 September 2020 Accepted 5 April 2021