Second, imposing additional assumptions about the gas composition can grant the inverse problem a unique solution. Suppose the sensor response changed from m op , at the operating gas composition x op , to m . Invoking the linear approximation in eqn. 2, the inverse problem is to find x that satisfies: J(x op )(x -x op ) = mm op =: ∆m. Because J(x op ) is fat for a non-injective (M < G) gas sensor array, eqn. 16 has infinite solutions (fewer equations than unknowns).