A recent thermal ghost imaging experiment by Wus 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.
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