A simple setup that is capable of performing the function of an optical XOR logic gate is proposed. The setup consists of two BaTiO3 self-pumped phase conjugators as its principal elements. The mechanism of the gate is based on the phenomenon of self-pumped phase conjugation and the suppression of it by ordinarily polarized beams. In this way, the two input channels of the system are not required to be mutually coherent. In addition to its use as an XOR gate, the setup can be used as an image subtractor. And, as in the case in which it is used as a logic gate, the two input images do not need to be mutually coherent.