The problem of gamma-ray imaging encountered in nuclear medicine diagnosis is considered and solved by using distributed-parameter filtering theory. The nature of the photon emission and counting processes call for a generalization and application of some recent results concerning the filtering of stochastic processes that modulate the rate (intensity) of doubly stochastic Poissonian counting processes. From a theoretic point of view the results of the paper actually fill in formally an existing gap between lumped and di3tributed-parameter filtering theory. Three illustrative examples are worked out to highlight many of the ideas developed.