期刊
INVERSE PROBLEMS
卷 38, 期 6, 页码 -出版社
IOP Publishing Ltd
DOI: 10.1088/1361-6420/ac601c
关键词
nonlinear inverse problems; inexact Newton regularization; Landweber iteration; two-point gradient method; uniformly convex penalty
资金
- Fundamental Research Funds for the Central Universities
- National Natural Science Foundation of China [11871180]
This paper generalizes inexact Newton regularization methods to solve nonlinear inverse problems and can handle various types of noise. The method has fast convergence through the inner scheme and accelerated version.
In this paper, we generalize inexact Newton regularization methods to solve nonlinear inverse problems from a reflexive Banach space to a Banach space. The image space is not necessarily reflexive so that the method can be used to deal with various types of noise such as the Gaussian noise and the impulsive noise. The method consists of an outer Newton iteration and an inner scheme which provides increments by applying the regularization technique to the local linearized equations. Under some assumptions, in particular, the reflexivity of the image space is not required, we present a novel convergence analysis of the inexact Newton regularization method with inner scheme defined by Landweber iteration. Furthermore, by employing a two-point gradient method as inner regularization scheme to accelerate the convergence, we propose an accelerated version of inexact Newton-Landweber method and present the detailed convergence analysis. The numerical simulations are provided to demonstrate the effectiveness of the proposed methods in handling different kinds of noise and the fast convergence of the accelerated method.
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