THRESHOLDING RULES AND ITERATIVE SHRINKAGE/THRESHOLDING ALGORITHM: A CONVERGENCE STUDY
Identifieur interne : 000255 ( Hal/Curation ); précédent : 000254; suivant : 000256THRESHOLDING RULES AND ITERATIVE SHRINKAGE/THRESHOLDING ALGORITHM: A CONVERGENCE STUDY
Auteurs : Matthieu Kowalski [France]Source :
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Abstract
Imaging inverse problems can be formulated as an optimization problem and solved thanks to algorithms such as forward-backward or ISTA (Iterative Shrinkage/Thresholding Algorithm) for which non smooth functionals with sparsity constraints can be minimized efficiently. However, the soft thresholding operator involved in this algorithm leads to a biased estimation of large coefficients. That is why a step allowing to reduce this bias is introduced in practice. Indeed, in the statistical community, a large variety of thresholding operators have been studied to avoid the biased estimation of large coefficients; for instance, the non negative Garrote or the the SCAD thresholding. One can associate a non convex penalty to these opera-tors. We study the convergence properties of ISTA, possibly relaxed, with any thresholding rule and show that they correspond to a semi-convex penalty. The effectiveness of this approach is illustrated on image inverse problems.
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However, the soft thresholding operator involved in this algorithm leads to a biased estimation of large coefficients. That is why a step allowing to reduce this bias is introduced in practice. Indeed, in the statistical community, a large variety of thresholding operators have been studied to avoid the biased estimation of large coefficients; for instance, the non negative Garrote or the the SCAD thresholding. One can associate a non convex penalty to these opera-tors. We study the convergence properties of ISTA, possibly relaxed, with any thresholding rule and show that they correspond to a semi-convex penalty. The effectiveness of this approach is illustrated on image inverse problems.</abstract></profileDesc></hal></record>Pour manipuler ce document sous Unix (Dilib)
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