Inexact half-quadratic optimization for image reconstruction

We present new global convergence results for half-quadratic optimization in the context of image reconstruction. In particular, we do not assume that the inner optimization problem is solved exactly and we include the problematic cases where the objective function is nonconvex and has a continuum o...

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Bibliographic Details
Main Authors: Robini, Marc, Yuemin Zhu, Xudong Lv, Wanyu Liu
Format: Conference Proceeding
Language:English
Subjects:
Approximation algorithms
conjugate gradient
Convergence
Gradient methods
Half-quadratic optimization
Image reconstruction
Linear programming
nonconvex optimization
Numerical models
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Summary:We present new global convergence results for half-quadratic optimization in the context of image reconstruction. In particular, we do not assume that the inner optimization problem is solved exactly and we include the problematic cases where the objective function is nonconvex and has a continuum of stationary points. The inexact algorithm is modeled by a set-valued map defined from the majorization-minimization interpretation of half-quadratic optimization, and our main convergence results are based on the Kurdyka-Lojasiewicz inequality. We also propose a practical implementation that uses the conjugate gradient method and whose efficiency is illustrated by numerical experiments.
ISSN:2381-8549
DOI:10.1109/ICIP.2016.7533013