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Iterative Algorithms in Compressive Sensing

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Over the past few years, $\ell_1$-minimization has become the most popular method to recover sparse vectors from incomplete linear measurements. However, simpler iterative algorithms such as Iterative Hard Thresholding present the same theoretical guarantees when the measurement matrix satisfies the restricted isometry property. In this talk, I will focus on iterative algorithms that converge in a finite number of iterations proportional to the sparsity level. This fact was observed only recently for (weak) Orthogonal Matching Pursuit. I will also demonstrate a similar result for Hard Thresholding Pursuit. Advantages of the latter algorithm will be recalled along the way.

This talk is part of the Applied and Computational Analysis series.

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