Sparse and redundant representations − an emerging and powerful model for signals − suggests that a data source
could be described as a linear combination of few atoms from a pre-specified and over-complete dictionary. This
model has drawn a considerable attention in the past decade, due to its appealing theoretical foundations, and
promising practical results it leads to. Many of the applications that use this model are formulated as a mixture
of l2-lp (p ≤ 1) optimization expressions. Iterated Shrinkage algorithms are a new family of highly effective
numerical techniques for handling these optimization tasks, surpassing traditional optimization techniques. In
this paper we aim to give a broad view of this group of methods, motivate their need, present their derivation,
show their comparative performance, and most important of all, discuss their potential in various applications.