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Iterative Algorithms in Compressive Sensing

Høisæther, Kristoffer Ulvik
Master thesis
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hoisaether_thesis.pdf (1.559Mb)
Year
2018
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http://urn.nb.no/URN:NBN:no-66034

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  • Anvendt matematikk og og mekanikk [207]
Abstract
The field of compressive sensing is a modern field in applied mathematics which receives a lot of attention. In this thesis, we will give some insight into the iterative algorithms used in compressive sensing. We will study in particular the primal-dual algorithm, as proposed by Chambolle and Pock, and Nesterov's algorithm, NESTA. In general, the primal-dual algorithm is a more traditional algorithm than NESTA. Nesterov proved that for general convex functions, the primal-dual algorithm cannot achieve a better convergence rate than O(1/k), where k is the number of iterations, whereas Nesterov's algorithm with general convex functions achieves a convergence rate of O(1/(k^2)).
 
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