@inproceedings{kowalski_thresholding_2014,
	title = {Thresholding {RULES} and iterative shrinkage/thresholding algorithm: {A} convergence study},
	shorttitle = {Thresholding {RULES} and iterative shrinkage/thresholding algorithm},
	doi = {10.1109/ICIP.2014.7025843},
	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 operators. 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.},
	language = {en},
	booktitle = {2014 {IEEE} {International} {Conference} on {Image} {Processing} ({ICIP})},
	author = {Kowalski, Matthieu},
	month = oct,
	year = {2014},
	note = {ISSN: 2381-8549},
	keywords = {\#Analysis, \#ICIP{\textgreater}14, /unread, Sparse approximation, nonnegative garrote, relaxed ISTA, semi convex optimization},
	pages = {4151--4155},
}

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