MR Quality Control: SNRHow do you measure signal-to-noise in an image?
|
|
Before reading this section you should be aware that there is no universally accepted method to measure the MR signal-to-noise ratio (SNR) applicable to all situations. Both the "signal" and the "noise" must be measured, but that is not as easy to accomplish as one might imagine!
Nature and Characteristics of Noise
For quality control purposes, we are concerned with random (background) noise, primarily thermal in nature, arising from radiofrequency coil resistance, electronic noise in the preamplifier, and dielectric and inductive losses in the imaged object. Random background noise should be distinguished from structured noise, such as that arising from ghosting, motion, filtering, and reconstruction. Structured noise is certainly important, particularly for SNR in living subjects, but is not the focus of this Q&A.
He we will restrict our analysis to measurements of signal and noise in and around a uniform phantom obtained from a 2D spin-echo pulse sequence. Experimental evidence supports the concept that random MR noise can be considered "white" (distributed equally across all frequencies) with an amplitude distribution that is approximately Gaussian.
Distribution of noise pixels under various conditions
Because region-of-interest (ROI) measurements are typically made on magnitude-reconstructed images, some correction to the statistics must take place. Recall that "raw" MR data is a complex number with real and imaginary parts. When converted to a magnitude only image, the pixel values corresponding to noise are no longer Gaussian, but skewed into a so-called Rician distribution. Fortunately, some simplification of the noise statistics occurs in two locations: a) in the center of the phantom where the SNR is intrinsically high, the noise can again be considered Gaussian; and b) in the air outside the phantom where the the pixel distribution follows the Rayleigh distribution, whose standard deviation is related to the standard deviation of the original Gaussian by a factor of √(2−π/2) ≈ 0.66.
Methods for Measuring SNR with Phantoms
The National Manufacturers Electrical Association (NEMA) provides several methods for measuring the SNR in a phantom, two of which are most commonly used.
A uniform phantom with regions of interest identified for measuring signal (S) and noise (N)
In the first method pictured right, a circular ROI to measure mean signal (S) is chosen that incorporates most of the phantom (but avoiding the edges). Random noise (N) is measured as the average standard deviation of pixel intensity from air from four square ROIs located at the corners of the image. (The location of these ROIs is to avoid structured noise from the phantom propagated along the phase and frequency axes). The measured SNR = S/N must then be multiplied by the 0.66 Rayleigh distribution correction factor to calculate the true SNR. If more than one receive coil is used for data collection, an additional correction factor of up to 8% (depending on number of coils) may also need to be applied.
|
A second NEMA method measures noise statistics within the phantom itself. A circular central ROI is defined as before. Two images are then obtained in the same location in rapid succession. Signal (S) is the mean pixel value within the ROI of these first two images. The two images are then subtracted from one another and the difference data analyzed. Ideally the proton signal from the phantom itself would be eliminated leaving only noise behind. The standard deviation of pixel values within the ROI of the subtracted image is an estimate of the random noise (assumed to be Gaussian). But because this calculation involves a difference operation, the true SNR must be corrected by a factor of 1/√2 ≈ 0.71. An additional multi-receive coil correction may also be necessary as in the first method.
|
Subtraction of two successively obtained magnitude images to estimate noise (N) within the phantom
|
References
Cárdenas-Blanco A, Tejos, Irarrazaval P, Cameron I. Noise in magnitude magnetic resonance images. Concepts Magn Reson Part A 2008; 32:409-416. [DOI Link]
Dietrich O, Raya JG, Reeder SB, et al. Measurement of signal-to-noise ratios in MR images: Influence of multi-channel coils, parallel imaging, and reconstruction filters. J Magn Reson Imaging 2007; 26: 375-385. [DOI Link]
Erdogmas D, Larsson EG, Yan R et al. Measuring the signal-to-noise ratio in magnetic resonance imaging: a caveat. Signal Processing 2004;84:1035–1040. [DOI Link]
Firbank MJ, Coulthard A, Harrison RM, Williams ED. A comparison of two methods for measuring the signal to noise ratio on MR images. Phys Med Biol 1999; 44: N261-4. [DOI Link]
Gudbjartsson H, Patz S. The Rician distribution of noisy MRI data. Magn Reson Med 1995; 34:910-914. [DOI Link]
McVeigh ER, Henkelman RM, Bronskill MJ. Noise and filtration in magnetic resonance imaging. Med Phys 1985; 12:586-591. [DOI Link]
National Manufacturers Electrical Association. MS1-2008 Determination of signal-to-noise ratio SNRin diagnostic magnetic resonance images (pdf), NEMA, Washington, DC. Can be downloaded for free or purchased in book form here.
National Manufacturers Electrical Association. MS 6-2008 (R2014). Determination of signal-to-noise ratio and image uniformity for single-channel non-volume coils diagnostic MR imaging (pdf).
NEMA, Washington, DC. Can be downloaded for free or purchased in book form here.
National Manufacturers Electrical Association MS 9-2008 (R2014). Characterization of phased array coils for diagnostic magnetic resonance images (pdf), NEMA, Washington, DC. Can be downloaded for free or purchased in book form here.
Rice SO. Mathematical analysis of random noise and appendixes. Bell Telephone Labs, 1952. (A technical report which contains Rice’s original landmark papers from 1944 and 1945 plus additional materials.)
Cárdenas-Blanco A, Tejos, Irarrazaval P, Cameron I. Noise in magnitude magnetic resonance images. Concepts Magn Reson Part A 2008; 32:409-416. [DOI Link]
Dietrich O, Raya JG, Reeder SB, et al. Measurement of signal-to-noise ratios in MR images: Influence of multi-channel coils, parallel imaging, and reconstruction filters. J Magn Reson Imaging 2007; 26: 375-385. [DOI Link]
Erdogmas D, Larsson EG, Yan R et al. Measuring the signal-to-noise ratio in magnetic resonance imaging: a caveat. Signal Processing 2004;84:1035–1040. [DOI Link]
Firbank MJ, Coulthard A, Harrison RM, Williams ED. A comparison of two methods for measuring the signal to noise ratio on MR images. Phys Med Biol 1999; 44: N261-4. [DOI Link]
Gudbjartsson H, Patz S. The Rician distribution of noisy MRI data. Magn Reson Med 1995; 34:910-914. [DOI Link]
McVeigh ER, Henkelman RM, Bronskill MJ. Noise and filtration in magnetic resonance imaging. Med Phys 1985; 12:586-591. [DOI Link]
National Manufacturers Electrical Association. MS1-2008 Determination of signal-to-noise ratio SNRin diagnostic magnetic resonance images (pdf), NEMA, Washington, DC. Can be downloaded for free or purchased in book form here.
National Manufacturers Electrical Association. MS 6-2008 (R2014). Determination of signal-to-noise ratio and image uniformity for single-channel non-volume coils diagnostic MR imaging (pdf).
NEMA, Washington, DC. Can be downloaded for free or purchased in book form here.
National Manufacturers Electrical Association MS 9-2008 (R2014). Characterization of phased array coils for diagnostic magnetic resonance images (pdf), NEMA, Washington, DC. Can be downloaded for free or purchased in book form here.
Rice SO. Mathematical analysis of random noise and appendixes. Bell Telephone Labs, 1952. (A technical report which contains Rice’s original landmark papers from 1944 and 1945 plus additional materials.)