A theoretical formalism for the interpretation of STM images of adsorbates is developed by approaching the calculation of the observed current as a transport problem in quantum statistical mechanics. The STM configuration is treated as a system of three groups of states - the substrate, the adsorbate and the tip - in contact with a thermal reservoir, with which it exchanges energy. A new definition of current is introduced, and shown to be related to that given in the traditional transfer Hamiltonian approach. The transport instrument used for the description is the stochastic Liouville equation, known to have the advantage of allowing the incorporation of thermal effects as well as arbitrary degree of coherence in the quantum transport. Some preliminary calculations of STM images of simple adsorbate models are presented. © 1992.