Edinburgh Research Explorer

Iterative hard thresholding for compressed sensing

Research output: Contribution to journalArticle

Related Edinburgh Organisations

Documents

Original languageEnglish
Pages (from-to)265-274
Number of pages10
JournalApplied and Computational Harmonic Analysis
Volume27
Issue number3
DOIs
Publication statusPublished - 2009

Abstract

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.

    Research areas

  • Algorithms, Compressed sensing, Sparse inverse problem, Signal recovery, Iterative hard thresholding

Download statistics

No data available

ID: 1822551