Methods of interpreting error estimates for grayscale image reconstructions

One representation of possible errors in a grayscale image reconstruction is as another grayscale image estimating potentially worrisome differences between the reconstruction and the actual "ground-truth" reality. Visualizations and summary statistics can aid in the interpretation of such a representation of error estimates. Visualizations include suitable colorizations of the reconstruction, as well as the obvious "correction" of the reconstruction by subtracting off the error estimates. The canonical summary statistic would be the root-mean-square of the error estimates. Numerical examples involving cranial magnetic-resonance imaging clarify the relative merits of the various methods in the context of compressed sensing. Unfortunately, the colorizations appear likely to be too distracting for actual clinical practice, and the root-mean-square gets swamped by background noise in the error estimates. Fortunately, straightforward displays of the error estimates and of the "corrected" reconstruction are illuminating, and the root-mean-square improves greatly after mild blurring of the error estimates; the blurring is barely perceptible to the human eye yet smooths away background noise that would otherwise overwhelm the root-mean-square.