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 Freeman's KIII, 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.