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Article Dans Une Revue SIAM Journal on Imaging Sciences Année : 2015

Generic Half-Quadratic Optimization for Image Reconstruction

Résumé

We study the global and local convergence of a generic half-quadratic optimization algorithm inspired from the dual energy formulation of Geman and Reynolds [IEEE Trans. Pattern Anal. Mach. Intell., 14 (1992), pp. 367--383]. The target application is the minimization of $C^{1}$ convex and nonconvex objective functionals arising in regularized image reconstruction. Our global convergence proofs are based on a monotone convergence theorem of Meyer [J. Comput. System Sci., 12 (1976), pp. 108--121]. Compared to existing results, ours extend to a larger class of objectives and apply under weaker conditions; in particular, we cover the case where the set of stationary points is not discrete. Our local convergence results use a majorization-minimization interpretation to derive an insightful characterization of the basins of attraction; this new perspective grounds a formal description of the intuitive water-flooding analogy. We conclude with image restoration experiments to illustrate the efficiency of the algorithm under various nonconvex scenarios.Read More: http://epubs.siam.org/doi/abs/10.1137/140987845
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Dates et versions

hal-01273364 , version 1 (12-02-2016)

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Marc C. Robini, Yuemin Zhu. Generic Half-Quadratic Optimization for Image Reconstruction. SIAM Journal on Imaging Sciences, 2015, 8 (3), pp.1752-1797. ⟨10.1137/140987845⟩. ⟨hal-01273364⟩
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