H. Takajo et al., Further study on the convergence property of the hybrid input-output algorithm used for phase retrieval, J OPT SOC A, 16(9), 1999, pp. 2163-2168
In our previous paper [J. Opt. Sec. Am. A 15, 2849 (1998)], we investigated
the behavior of the hybrid input-output algorithm (HIO) used for phase ret
rieval and showed that the HIO with an infinitesimally small feedback param
eter has two abilities that are extremely important in finding a solution:
the ability to locate an output-stagnation object and the ability to emerge
from an output-stagnation object if it is not a solution. The behavior of
the HIO is analyzed further, and an additional aspect is demonstrated that
is also important in finding a solution. That is, outside the support of th
e input object of the HIO, the output-object values outside the support tha
t have been produced so far accumulate so that the probability is conjectur
ed to be extremely low that the HIO will fall into a periodic state. On the
other hand, it is also demonstrated that this aspect of the HIO is not usu
ally effective in the combination algorithm composed of the HIO and the err
or-reduction algorithm. To give credibility to our arguments, we show resul
ts that were obtained by reexamining the examples adopted in Seldin and Fie
nup's numerical experiments [J. Opt. Sec. Am. A 7, 412 (1990)]. (C) 1999 Op
tical Society of America [S0740-3232(99)00309-9] OCIS codes: 100.5070, 100.
3010, 100.2000.