  A recent thermal ghost imaging experiment by Wu's group constructed positive
and negative images using a novel algorithm. This algorithm allows to form the
images with use of partial measurements from the reference arm, even which
never passes through the object, conditioned on the object arm. In this paper,
we present a simple theory which explains the experimental observation, and
provides an in-depth understanding of conventional ghost imaging. In
particular, we theoretically show that the visibility of formed images through
such an algorithm is not bounded by the standard value 1/3. In fact, it can
ideally grow up to unity (with reduced imaging quality). Thus, the algorithm
described here not only offers an alternative way to decode spatial correlation
of thermal light, but also mimics a "bandpass filter" to remove the constant
background such that the visibility or imaging contrast is improved. We further
show that conditioned on one still object present in the test arm, it is
possible to construct its image by sampling the available reference data.
