Non-iterative implementation of a class of iterative signal restoration algorithms

D. O. Walsh, P. A. Delaney, M. W. Marcellin

Research output: Contribution to journalConference article

3 Scopus citations

Abstract

In this paper, we show that a class of iterative signal restoration algorithms, which includes as a special case the discrete Gerchberg-Papoulis algorithm, can always be implemented directly (i.e., non-iteratively). In the exactly- and over-determined cases, the iterative algorithm always converges to a unique least squares solution. In the under-determined case, it is shown that the iterative algorithm always converges to the sum of a unique minimum norm solution and a term dependent on initial conditions. For the purposes of early termination, it is shown that the output of the iterative algorithm at the rth iteration can be computed directly using a singular value decomposition-based algorithm. The computational requirements of various iterative and non-iterative implementations are discussed, and the effect of the relaxation parameter on the regularization capability of the iterative algorithm is investigated.

Original languageEnglish (US)
Pages (from-to)1672-1675
Number of pages4
JournalICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume3
StatePublished - Jan 1 1996
EventProceedings of the 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP. Part 1 (of 6) - Atlanta, GA, USA
Duration: May 7 1996May 10 1996

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

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