The bias/variance trade-off when estimating the MR signal magnitude from the complex average of repeated measurements

The signal-dependent bias of MR images has been considered a hindrance to visual interpretation almost since the beginning of clinical MRI. Over time, a variety of procedures have been suggested to produce less-biased images from the complex average of repeated measurements. In this work, we re-evaluate these approaches using first a survey of previous estimators in the MRI literature, then a survey of the methods statisticians employ for our specific problem. Our conclusions are substantially different from much of the previous work: first, removing bias completely is impossible if we demand the estimator have bounded variance; second, reducing bias may not be beneficial to image quality.