Bajkova's generalized maximum entropy method for reconstruction of com
plex signals is further generalized through the use of Kullback-Leible
r cross entropy. This permits a priori information in the form of bias
functions to be inserted into the algorithm, with resulting benefits
to reconstruction quality. Also, the cross-entropy term is imbedded wi
thin an overall maximum a posteriori probability approach that include
s a noise-rejection term. A further modification is transformation of
the large two-dimensional problem arising from modest-sized two-dimens
ional images into a sequence of one-dimensional problems. Finally the
added operation of three-point median window filtration of each interm
ediary one-dimensional output is shown to suppress edge-top overshoots
while augmenting edge gradients. Applications to simulated complex im
ages are shown.