Properties of subgradient projection iteration when applying to linear imaging system

In this paper, the subgradient projection iteration is used to find an approximation solution of a weighted least-squares problem with respect to linear imaging system. Instead of an exact or approximate line search in each iteration, the step length in this paper is fixed by the weighted least-squa...

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Bibliographic Details
Published in:Optimization letters Vol. 13; no. 6; pp. 1285 - 1297
Main Author: Wang, Caifang
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2019
Subjects:
Computational Intelligence
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Operations Research/Decision Theory
Optimization
Original Paper
Simulation
Subgradient projection algorithm
Weighted singular value decomposition
Linear system
Convergence condition
Decreasing property
ISSN:1862-4472, 1862-4480
Online Access:Get full text
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Summary:In this paper, the subgradient projection iteration is used to find an approximation solution of a weighted least-squares problem with respect to linear imaging system. Instead of an exact or approximate line search in each iteration, the step length in this paper is fixed by the weighted least-square function and the current iteration. Using weighted singular value decomposition, we estimate the bounds of step length. Consequently, we provide the decreasing property and the sufficient condition for convergence of the iterative algorithm. Furthermore, we perform a numerical experiment on a two dimensional image reconstruction problem to confirm the validity of this subgradient projection iteration.
ISSN:1862-4472
1862-4480
DOI:10.1007/s11590-018-1321-3