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Träfflista för sökning "L773:0163 0563 OR L773:1532 2467 srt2:(2020-2021)"

Sökning: L773:0163 0563 OR L773:1532 2467 > (2020-2021)

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1.
  • Aspri, A., et al. (författare)
  • A Data-Driven Iteratively Regularized Landweber Iteration
  • 2020
  • Ingår i: Numerical Functional Analysis and Optimization. - : Taylor and Francis Inc.. - 0163-0563 .- 1532-2467.
  • Tidskriftsartikel (refereegranskat)abstract
    • We derive and analyze a new variant of the iteratively regularized Landweber iteration, for solving linear and nonlinear ill-posed inverse problems. The method takes into account training data, which are used to estimate the interior of a black box, which is used to define the iteration process. We prove convergence and stability for the scheme in infinite dimensional Hilbert spaces. These theoretical results are complemented by some numerical experiments for solving linear inverse problems for the Radon transform and a nonlinear inverse problem for Schlieren tomography. 
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2.
  • Mirzapour, Mahdi, et al. (författare)
  • Convergence and Semi-Convergence of a Class of Constrained Block Iterative Methods
  • 2021
  • Ingår i: Numerical Functional Analysis and Optimization. - : TAYLOR & FRANCIS INC. - 0163-0563 .- 1532-2467. ; 42:14, s. 1718-1746
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper, we analyze the convergence properties of projected non-stationary block iterative methods (P-BIM) aiming to find a constrained solution to large linear, usually both noisy and ill-conditioned, systems of equations. We split the error of the kth iterate into noise error and iteration error, and consider each error separately. The iteration error is treated for a more general algorithm, also suited for solving split feasibility problems in Hilbert space. The results for P-BIM come out as a special case. The algorithmic step involves projecting onto closed convex sets. When these sets are polyhedral, and of finite dimension, it is shown that the algorithm converges linearly. We further derive an upper bound for the noise error of P-BIM. Based on this bound, we suggest a new strategy for choosing relaxation parameters, which assist in speeding up the reconstruction process and improving the quality of obtained images. The relaxation parameters may depend on the noise. The performance of the suggested strategy is shown by examples taken from the field of image reconstruction from projections.
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  • Resultat 1-2 av 2

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