Summary: Inspired by the ability of the olfactory bulb to enhance the contrast between odor representations, we propose a new Hebbian learning rule that is able to increase the separability of odor patterns from gas sensor arrays. The proposed learning rule employs a Hebbian term to build associations within odors and an anti-Hebbian term to reduce correlated activity across odors. In addition to increasing the separability of patterns, the new learning rule can also achieve odor background suppression when combined with a habituation term. These two functions are demonstrated on \textit{W. Freeman}'s KIII [Mass action in the nervous system: Examination of neurophysiological basis of adaptive behavior through the EEG. (1975)], a neurodynamics model of the olfactory system. The system is first characterized on synthetic data, and also validated on experimental data from an array of chemical sensors exposed to organic solvents.