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 language||English (US)|
|Number of pages||1|
|Journal||IEEE Transactions on Signal Processing|
|State||Published - Dec 1 1996|
ASJC Scopus subject areas
- Signal Processing
- Electrical and Electronic Engineering