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How to use the iterative hard thresholding algorithm

Abstract : Several computationally efficient algorithms have been shown to offer near optimal recovery of sparse signals from a small number of linear measurements. However, whilst many of the methods have similar guarantees whenever the measurements satisfy the so called restricted isometry property, empirical performance of the methods can vary significantly in a regime in which this condition is not satisfied. We here modify the Iterative Hard Thresholding algorithm by including an automatic step-size calculation. This makes the method independent from an arbitrary scaling of the measurement system and leads to a method that shows state of the art empirical performance. What is more, theoretical guarantees derived for the unmodified algorithm carry over to the new method with only minor changes.
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https://hal.inria.fr/inria-00369654
Contributor : Ist Rennes <>
Submitted on : Friday, March 20, 2009 - 3:43:50 PM
Last modification on : Thursday, December 13, 2018 - 8:02:02 PM
Long-term archiving on: : Thursday, June 10, 2010 - 5:52:08 PM

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  • HAL Id : inria-00369654, version 1

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Thomas Blumensath, Michael E Davies. How to use the iterative hard thresholding algorithm. SPARS'09 - Signal Processing with Adaptive Sparse Structured Representations, Inria Rennes - Bretagne Atlantique, Apr 2009, Saint Malo, France. ⟨inria-00369654⟩

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