and Alan C . Bovik ] Mean Squared Error : Love It or Leave It ?

or more than 50 years, the mean-squared error (MSE) has been the dominant quantitative performance metric in the field of signal processing. It remains the standard criterion for the assessment of signal quality and fidelity; it is the method of choice for comparing competing signal processing methods and systems, and, perhaps most importantly, it is the nearly ubiquitous preference of design engineers seeking to optimize signal processing algorithms. This is true despite the fact that in many of these applications, the MSE exhibits weak performance and has been widely criticized for serious shortcomings, especially when dealing with perceptually important signals such as speech and images. Yet the MSE has exhibited remarkable staying power, and prevailing attitudes towards the MSE seem to range from " it's easy to use and not so bad " to " everyone else uses it. " So what is the secret of the MSE—why is it still so popular? And is this popularity misplaced? What is wrong with the MSE when it does not work well? Just how wrong is the MSE in these cases? If not the MSE, what else can be used? These are the questions we'll be concerned with in this article. Our backgrounds are primarily in the field of image processing, where the MSE has a particularly bad reputation, but where, ironically, it is used nearly as much as in other areas of signal processing. Our discussion will often deal with the role of the MSE (and alternative methods) for processing visual signals. Owing to the poor performance of the MSE as a visual metric, interesting alternatives are arising in the image processing field. Our goal is to stimulate fruitful thought and discussion regarding the role of the MSE in processing other types of signals. More specifically, we hope to inspire signal processing engineers to rethink whether the MSE is truly the criterion of choice in their own theories and applications, and whether it is time to look for alternatives. [ A new look at signal fidelity measures ]