The University of Southampton
University of Southampton Institutional Repository

Iterative hard thresholding for compressed sensing

Blumensath, T. and Davies, M.E. (2009) Iterative hard thresholding for compressed sensing Applied and Computational Harmonic Analysis, 27, (3), pp. 265-274. (doi:10.1016/j.acha.2009.04.002).

Record type: Article


Compressed sensing is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper we present a theoretical analysis of the iterative hard thresholding algorithm when
applied to the compressed sensing recovery problem. We show that the algorithm has the following properties (made more precise in the main text of the paper)
• It gives near-optimal error guarantees.
• It is robust to observation noise.
• It succeeds with a minimum number of observations.
• It can be used with any sampling operator for which the operator and its adjoint can be computed.
• The memory requirement is linear in the problem size.
• Its computational complexity per iteration is of the same order as the application of the measurement operator or its adjoint.
• It requires a fixed number of iterations depending only on the logarithm of a form of signal to noise ratio of the signal.
• Its performance guarantees are uniform in that they only depend on properties of the sampling operator and signal sparsity

PDF BDIHT.pdf - Other
Restricted to Repository staff only
Download (179kB)

More information

Published date: November 2009
Keywords: algorithms, compressed sensing, sparse inverse problem, signal
Organisations: Other, Signal Processing & Control Grp


Local EPrints ID: 142507
ISSN: 1063-5203
PURE UUID: 57de7036-0fdf-4d46-b37d-9356fe5a5b36

Catalogue record

Date deposited: 31 Mar 2010 15:52
Last modified: 18 Jul 2017 23:11

Export record


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.