The University of Southampton
University of Southampton Institutional Repository

Normalised iterative hard thresholding: guaranteed stability and performance

Blumensath, Thomas and Davies, Mike E. (2010) Normalised iterative hard thresholding: guaranteed stability and performance IEEE Journal of Selected Topics in Signal Processing, 4, (2), pp. 298-309. (doi:10.1109/JSTSP.2010.2042411).

Record type: Article


Sparse signal models are used in many signal processing applications. The task of estimating the sparsest coefficient vector in these models is a combinatorial problem and efficient, often suboptimal strategies have to be used. Fortunately, under certain conditions on the model, several algorithms could be shown to efficiently calculate near-optimal solutions. In this paper, we study one of these methods, the so-called Iterative Hard Thresholding algorithm. While this method has strong theoretical performance guarantees whenever certain theoretical properties hold, empirical studies show that the algorithm's performance degrades significantly, whenever the conditions fail. What is more, in this regime, the algorithm also often fails to converge. As we are here interested in the application of the method to real world problems, in which it is not known in general, whether the theoretical conditions are satisfied or not, we suggest a simple modification that guarantees the convergence of the method, even in this regime. With this modification, empirical evidence suggests that the algorithm is faster than many other state-of-the-art approaches while showing similar performance. What is more, the modified algorithm retains theoretical performance guarantees similar to the original algorithm.

PDF BD_NIHT09.pdf - Other
Download (277kB)

More information

Published date: 15 March 2010
Organisations: Signal Processing & Control Grp


Local EPrints ID: 142499
PURE UUID: 0e046b14-e93a-4992-a51a-281f94d3dd00

Catalogue record

Date deposited: 31 Mar 2010 14:56
Last modified: 18 Jul 2017 23:11

Export record



Author: Mike E. Davies

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton:

ePrints Soton supports OAI 2.0 with a base URL of

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.