Geodesic
A new two-step iteration method for discrete ill-posed problems and image restoration
Filomat, Tome 36 (2022) no. 6, p. 1837

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DOI

In this study, for the augmented linear system of discrete ill-posed problems we establish a new two-step (NTS) iteration method containing a parameter and a parameter matrix, which is based on the Hermitian and skew-Hermitian splitting (HSS) and the upper and lower triangular splitting (ULT) of the coefficient matrix. Then, we theoretically study its convergence properties and determine its optimal iteration parameters. It is seen that the NTS method converges faster when the parameters are chosen properly. Experimental examples are carried out to further validate the effectiveness and accuracy of the new method compared to the newly developed methods in terms of the numerical performance and image recovering quality.
DOI : 10.2298/FIL2206837C
Classification : 65F10, 65F50, 65N20
Keywords: Hermitian and skew-Hermitian splitting, Upper and lower triangular splitting, Iteration method, Image restoration, Ill-posed problems 
Jingjing Cui; Guohua Peng; Quan Lu; Zhengge Huang. A new two-step iteration method for discrete ill-posed problems and image restoration. Filomat, Tome 36 (2022) no. 6, p. 1837 . doi: 10.2298/FIL2206837C
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     title = {A new two-step iteration method for discrete ill-posed problems and image restoration},
     journal = {Filomat},
     pages = {1837 },
     year = {2022},
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     doi = {10.2298/FIL2206837C},
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     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2206837C/}
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