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Properties of subgradient projection iteration when applying to linear imaging system

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Abstract

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.

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Acknowledgements

Caifang Wang is supported by National Natural Science Foundation of China (11401372).

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  1. Department of Mathematics, Shanghai Maritime University, Shanghai, China

    Caifang Wang

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  1. Caifang Wang
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Correspondence to Caifang Wang.

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Wang, C. Properties of subgradient projection iteration when applying to linear imaging system. Optim Lett 13, 1285–1297 (2019). https://doi.org/10.1007/s11590-018-1321-3

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