Compensating for gain in objective quality estimation algorithms

When objectively estimating speech, audio, or video quality, it is often necessary to compensate for the system gain or to "gain match" two or more signals. One can take three views of a system, leading to three different definitions of gain, and three different gain compensation solutions: one that minimizes distortion, one that matches input-output power, and one that maximizes signal-to-distortion ratio. We derive these three solutions, describe the algebraic and geometric relationships between them, and provide a generalized result that subsumes all three. We provide examples showing that these three solutions do differ in practical quality estimation situations. We also report some of the gain compensation choices found in the quality estimation literature.