A new mathematical technique for information fusion based on random sets, developed and described by Goodman, Mahler and Nguyen (The Mathematics of Data Fusion, Kluwer, 1997) can be useful for estimation of functional brian images. Many image estimation algorithms employ prior models that incorporate general knowledge about sizes, shapes and locations of brain regions. Recently, algorithms have been proposed using specific prior knowledge obtained from other imaging modalities (for example, Bowsher, et al., IEEE Trans. Medical Imaging, 1996). However, there is more relevant information than is presently used. A technique that permits use of additional prior information about activity levels would improve the quality of prior models, and hence, of the resulting image estimate. The use of random sets provides this capability because it allows seemingly non-statistical (or ambiguous) information such as that contained in inference rules to be represented and combined with observations in a single statistical model, corresponding to a global joint density. This paper illustrates the use of this approach by constructing an example global joint density function for brain functional activity from measurements of functional activity, anatomical information, clinical observations and inference rules. The estimation procedure is tested on a data phantom with Poisson noise.