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Editorials |
1 From the Department of Diagnostic Radiology, Philipps University Marburg, University Hospital Giessen and Marburg, Baldinger Strasse, 35033 Marburg, Germany; and Department of Radiology, the Ohio State University, Columbus, Ohio. Received December 18, 2006; final version accepted February 12, 2007. Address correspondence to the author (e-mail: heverhag{at}mailer.uni-marburg.de).
Any experiment measuring signal intensity or contrast in cross-sectional imaging also needs to provide an estimation of the image noise. Every year, thousands of manuscripts that include noise estimation are submitted to various imaging and subspecialty journals.
There are many different methods to help provide an estimate of the noise in cross-sectional magnetic resonance (MR) images. These methods are described in textbooks, but there is no overview providing a guideline to authors on how to perform noise measurements or estimations. In this editorial, I will indicate what I believe are the advantages and disadvantages of those various methods. In addition, I will offer scenarios in which the different methods can be applied.
In general, image noise is derived from random fluctuations in the receiver coil electronics and the sample being imaged (1). Even though there are many other sources of image noise, such as ghosting due to moving spins or digitization noise, these sources should be minimized in an ideal experiment. White noise is independent of the position of voxels in the image (2). Therefore, the standard deviation of a voxel's signal over a homogeneous region of a tissue of interest in the image is a good estimate of the image noise. However, this is only true if systematic variations, such as Gibbs ringing, are absent (3).
The only true measurement of image noise is to acquire the same image twice and subtract the two images from each other. The remaining signal, average value or standard deviation, is the actual image noise. This method can easily be applied to static brain imaging, imaging of extremities, or MR experiments involving samples.
However, it is not always possible to acquire the same measurement twice. Time-sensitive acquisitions, in contrast material–enhanced studies (4), functional studies (5), or studies with limited imaging time (6), are prime examples of MR measurements that cannot be repeated to derive the image noise. In these cases, image noise can be estimated with various methods.
The most commonly used method is the measurement of signal intensity and its standard deviation in the air surrounding the imaging volume (3). Usually, the standard deviation is used as an estimate for image noise. However, such a setting is vulnerable to artifacts that can artificially increase the standard deviation. If no artifacts are present, this method results in a low estimate of image noise. It can be easily applied in body regions that do not exhibit motion such as the head or the extremities.
However, the investigator has to make sure that such artifacts are avoided. It should be easy in the case of simple foldover or obvious ghosting artifacts. But slight motion, of the eyes, for example, sometimes leads to subtle ghosting not readily recognizable. Here, special care has to be taken that the noise is not artificially increased. This method can be readily applied to dynamic contrast-enhanced (7), time-sensitive breath-hold thoracic or abdominal (4), and functional (8) studies.
The second method is the measurement of the standard deviation of signal intensity, either in the targeted tissue or, in the case of contrast-enhanced studies, tissue close to the target tissue. Here, the estimate of image noise will be higher but closer to the actual image noise. The investigator has to take special care that the region of interest in which the noise is measured is homogeneous and does not contain tissues with different image properties. If the region of interest includes tissues with different properties, the standard deviation would no longer represent the image noise but rather the signal differences of the included tissues. Again, it is mandatory to avoid regions that are affected by artifacts as outlined above. If artifacts cannot be avoided, this method is not applicable for noise estimation.
Due diligence has to be applied in artifact-prone investigations such as neurofunctional, diffusion-weighted, or dynamic susceptibility-weighted applications. These applications provide source images that are compromised by artifacts throughout the entire field of view. Usually, meaningful noise measurements cannot be obtained. However, in such scenarios image noise cannot be assessed only as white noise. All other sources of image noise, such as motion, susceptibility, ghosting, and others, have to be considered. Therefore, the region for noise estimation has to be chosen carefully, and the reasons for this choice have to be explained.
Parallel imaging, characterized by a spatially varying signal-to-noise ratio, also needs special attention when calculating the ratio. Many authors claim that no meaningful signal-to-noise ratio can be measured when parallel imaging methods, such as sensitivity encoding of spatial harmonics (9) or simultaneous acquisition of spatial harmonics (10), are applied. Noise levels in the reconstructed images largely depend on the sensitivity profiles of the receiver coils and increase with the acceleration factors employed. High constant magnetic induction field (B0) MR imaging (7 T and higher) provides a similar challenge since the radio frequency field strength (B1) is no longer homogeneous throughout the image. Therefore, the signal and the noise vary spatially throughout the image.
Consequently, conventional noise estimation in a homogeneous region outside of the imaged object can not be obtained since the noise distribution is no longer homogeneous. However, several authors have developed image reconstruction methods that make signal-to-noise ratio measurements feasible and applicable (11).
For both scenarios, the most practical method might be the measurement of a homogeneous region close to the site of signal intensity measurement. While the noise is not distributed homogeneously throughout the image, it is a good estimate of the noise in close proximity to the site of signal intensity measurement. Therefore, a signal-to-noise ratio cannot be calculated as a characteristic for the entire image but can be calculated as a local property characterizing the signal quality, with respect to local noise levels.
In conclusion, several methods of noise measurement and estimation exist. Prior to each experiment setup, investigators need to assess which method of noise measurement would be feasible for their study and plan their experiments accordingly. In the description of their methods for publication, the authors should explain which method was used and why they chose to use it.
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  R.P. Lim, M. Shapiro, E.Y. Wang, M. Law, J.S. Babb, L.E. Rueff, J.S. Jacob, S. Kim, R.H. Carson, T.P. Mulholland, et al. 3D Time-Resolved MR Angiography (MRA) of the Carotid Arteries with Time-Resolved Imaging with Stochastic Trajectories: Comparison with 3D Contrast-Enhanced Bolus-Chase MRA and 3D Time-Of-Flight MRA AJNR Am. J. Neuroradiol., November 1, 2008; 29(10): 1847 - 1854. [Abstract] [Full Text] [PDF]
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