TITLE:      Non-iterative implementation of a class of iterative 
	    signal restoration algorithms
AUTHORS:    D. O. Walsh, P. A. Delaney, and M. W. Marcellin
CONFERENCE: International Conference on Acoustics, Speech, and 
	    Signal Processing, Atlanta, Georgia, May 1996.
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 r{th} 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.