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 language | English (US) |
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Pages (from-to) | 1672-1675 |
Number of pages | 4 |
Journal | ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings |
Volume | 3 |
State | Published - 1996 |
Event | Proceedings of the 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP. Part 1 (of 6) - Atlanta, GA, USA Duration: May 7 1996 → May 10 1996 |
ASJC Scopus subject areas
- Software
- Signal Processing
- Electrical and Electronic Engineering