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

• Published in: Magnetic resonance in medicine 2011-11, Vol.66 (5), p.1456-1467
• Main Authors: Tisdall, M. Dylan, Lockhart, Richard A., Atkins, M. Stella
• Format: Article
• Language: English
• Subjects: Bayes Theorem; Bias; Computers; denoising; image bias; Likelihood Functions; Magnetic Resonance Imaging - methods; Mathematics; maximum likelihood estimate; nuisance parameters; Signal-To-Noise Ratio
• ISSN: 0740-3194; 1522-2594
• DOI: 10.1002/mrm.22910

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. Magn Reson Med, 2011. © 2011 Wiley Periodicals, Inc.