Noniterative Implementation of a Class of Iterative Signal Restoration Algorithms

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

Research output: Contribution to journalArticlepeer-review

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., noniteratively). In the exactly and overdetermined cases, the iterative algorithm always converges to a unique least squares solution. In the underdetermined 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 noniterative implementations are dicussed, and the effect of the relaxation parameter on the regularization capability of the iterative algorithm is investigated.

Original languageEnglish (US)
Number of pages1
JournalIEEE Transactions on Signal Processing
Volume44
Issue number5
StatePublished - Dec 1 1996

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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