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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 2p (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.

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This paper considers the problem of finding a landing spot for a drone in a dense urban environment. The conflicting requirements of fast exploration and high resolution are solved using a multi-resolution approach, by which visual information is collected by the drone at decreasing altitudes so that the spatial resolution of the acquired images increases monotonically. A probability distribution is used to capture the uncertainty of the decision process for each terrain patch. The distributions are updated as information from different altitudes is collected. When the confidence level for one of the patches becomes larger than a prespecified threshold, suitability for landing is declared. One of the main building blocks of the approach is a semantic segmentation algorithm that attaches probabilities to each pixel of a single view. The decision algorithm combines these probabilities with a priori data and previous measurements to obtain the best estimates. Feasibility is illustrated by presenting several examples generated by a realistic closed-loop simulator.