![](bg6.png)
converge any more. Obviously, the optimal
algorithm is in the beginning part of the iteration, the
algorithm needs to follow the adaptive relaxation
property and later to follow the iterative algorithm.
Figure 5: Comparison of the convergence properties
between the GS algorithm, the iterative algorithm, and
algorithm with adaptive relaxation.
Finally, in Figure 6, we presented the reconstructed
algorithm after 100 iterations using the iterative
algorithm. As we had given the justification, the
algorithm converges and the reconstructed signal
actually converges to the desired signal.
Figure 6: An example that shows the convergence
property of the iterative algorithm. (a) The original image
and (b) the reconstructed image after 100 iterations using
the iterative algorithm.
5 CONCLUSIONS
In this paper we considered the problem of
iteratively reconstructing a one-dimensional or a
two-dimensional signal from a pair of Fourier
intensities: the intensity of the signal along with the
intensity of another signal that is related by the
addition of a known reference signal. After we
present the uniqueness of the solution briefly, we
presented a simple proof that the iterative algorithm
converges the desired original signal, which is
assumed to be unknown. The algorithm combined
with the iterative algorithm and the adaptive
relaxation algorithm converges fast in the beginning
part and however goes saturated fastly also. Future
work may be the evaluating the robustness of the
algorithms to noise in the measured intensities and
methods of improving the convergence properties of
the constrained iterative algorithm.
ACKNOWLEDGEMENTS
This work was supported by the Korea Research
Foundation Grant funded by the Korean
Government (2009-0072495).
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