  To extract the maximum information about the object from a series of binary
samples in ghost imaging applications, we propose and demonstrate a framework
for optimizing the performance of ghost imaging with binary sampling to
approach the results without binarization. The method is based on maximizing
the information content of the signal arm detection, by formulating and solving
the appropriate parameter estimation problem - finding the binarization
threshold that would yield the reconstructed image with optimal Fisher
information properties. Applying the 1-bit quantized Poisson statistics to a
ghost-imaging model with pseudo-thermal light, we derive the fundamental limit,
i.e., the Cramer-Rao lower bound, as the benchmark for the evaluation of the
accuracy of the estimator. Our theoertical model and experimental results
suggest that, with the optimal binarization threshold, coincident with the
statistical mean of all bucket samples, and large number of measurements, the
performance of binary sampling GI can approach that of the ordinary one without
binarization.
