Mean squared error: Love it or leave it? A new look at Signal Fidelity Measures

In this article, we have reviewed the reasons why we (collectively) want to love or leave the venerable (but perhaps hoary) MSE. We have also reviewed emerging alternative signal fidelity measures and discussed their potential application to a wide variety of problems. The message we are trying to send here is not that one should abandon use of the MSE nor to blindly switch to any other particular signal fidelity measure. Rather, we hope to make the point that there are powerful, easy-to-use, and easy-to-understand alternatives that might be deployed depending on the application environment and needs. While we expect (and indeed, hope) that the MSE will continue to be widely used as a signal fidelity measure, it is our greater desire to see more advanced signal fidelity measures being used, especially in applications where perceptual criteria might be relevant. Ideally, the performance of a new signal processing algorithm might be compared to other algorithms using several fidelity criteria. Lastly, we hope that we have given further motivation to the community to consider recent advanced signal fidelity measures as design criteria for optimizing signal processing algorithms and systems. It is in this direction that we believe that the greatest benefit eventually lies.