TY - JOUR
T1 - Regularization of inverse problems by two-point gradient methods in Banach spaces
AU - Zhong, Min
AU - Wang, Wei
AU - Jin, Qinian
N1 - Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2019/11/1
Y1 - 2019/11/1
N2 - In this paper, we propose and analyze a two-point gradient method for solving inverse problems in Banach spaces which is based on the Landweber iteration and an extrapolation strategy. The method allows to use non-smooth penalty terms, including the L1-like and the total variation-like penalty functionals, which are significant in reconstructing special features of solutions such as sparsity and piecewise constancy in practical applications. The design of the method involves the choices of the step sizes and the combination parameters which are carefully discussed. Numerical simulations are presented to illustrate the effectiveness of the proposed method.
AB - In this paper, we propose and analyze a two-point gradient method for solving inverse problems in Banach spaces which is based on the Landweber iteration and an extrapolation strategy. The method allows to use non-smooth penalty terms, including the L1-like and the total variation-like penalty functionals, which are significant in reconstructing special features of solutions such as sparsity and piecewise constancy in practical applications. The design of the method involves the choices of the step sizes and the combination parameters which are carefully discussed. Numerical simulations are presented to illustrate the effectiveness of the proposed method.
UR - http://www.scopus.com/inward/record.url?scp=85069938913&partnerID=8YFLogxK
U2 - 10.1007/s00211-019-01068-0
DO - 10.1007/s00211-019-01068-0
M3 - Article
SN - 0029-599X
VL - 143
SP - 713
EP - 747
JO - Numerische Mathematik
JF - Numerische Mathematik
IS - 3
ER -