Abstract
In this paper, we propose a fast adaptive algorithm for solving nonlinear inverse problems in Hilbert spaces. The iterative process of the proposed method combines classical two point gradient method and adaptive accelerate strategy. In practice, it is often encountered that the reconstruction solution has special feature, such as sparsity and slicing smoothness. To capture the special feature of solution, convex functions are utilized to be penalty terms in iterative format. Meanwhile, a complete convergence analysis is given to show the theoretical rationality of the algorithm. The numerical simulations are provided to demonstrate the effectiveness and acceleration effect of the proposed method.
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01 September 2023
This article has been retracted. Please see the Retraction Notice for more detail: https://doi.org/10.1007/s40314-023-02439-y
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (Nos. 62072157, 61802116), the Key Technologies Research and Development Program of Henan Province (Nos. 222102210110, 232102210190, 232102211028) and the Natural Science Foundation of Henan Province (No. 202300410102).
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Communicated by Kelly Cristina Poldi.
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Ren, G., Gao, G. RETRACTED ARTICLE: A fast adaptive algorithm for nonlinear inverse problems with convex penalty. Comp. Appl. Math. 42, 188 (2023). https://doi.org/10.1007/s40314-023-02316-8
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DOI: https://doi.org/10.1007/s40314-023-02316-8