Original Research

Practical Signal-to-Noise Ratio Quantification forSensitivity Encoding: Application to CoronaryMR Angiography

Jing Yu, PhD,1,2 Harsh Agarwal, PhD,2 Matthias Stuber, PhD,2,3

and Michael Schar, MD2,4*

Purpose: To develop and evaluate a practical method forthe quantification of signal-to-noise ratio (SNR) on coro-nary MR angiograms (MRA) acquired with parallelimaging.

Materials and Methods: To quantify the spatially varyingnoise due to parallel imaging reconstruction, a newmethod has been implemented incorporating image dataacquisition followed by a fast noise scan during which ra-diofrequency pulses, cardiac triggering and navigator gat-ing are disabled. The performance of this method wasevaluated in a phantom study where SNR measurementswere compared with those of a reference standard (multi-ple repetitions). Subsequently, SNR of myocardium andposterior skeletal muscle was determined on in vivohuman coronary MRA.

Results: In a phantom, the SNR measured using the pro-posed method deviated less than 10.1% from the refer-ence method for small geometry factors (�2). In vivo, thenoise scan for a 10 min coronary MRA acquisition wasacquired in 30 s. Higher signal and lower SNR, due tospatially varying noise, were found in myocardium com-pared with posterior skeletal muscle.

Conclusion: SNR quantification based on a fast noisescan is a validated and easy-to-use method when appliedto three-dimensional coronary MRA obtained with parallelimaging as long as the geometry factor remains low.

Key Words: SNR measurement; parallel imaging; coro-nary MRA; phased array coils; image noiseJ. Magn. Reson. Imaging 2011; 33:1330–1340.VC 2011 Wiley-Liss, Inc.

ACCURATE QUANTIFICATION OF signal-to-noiseratio (SNR) is essential for objective evaluation of MRimages acquired with different hardware, imaging pro-tocols, and reconstruction methods. Numerous scien-tific and clinical studies strongly depend on objectiveend-points including signal and noise quantification.The choice of a proper SNR measurement approach istherefore often a critical component of the experimen-tal setup (1) and the analysis.

One of the most commonly used methods to mea-sure SNR includes the division of the average signalfrom a region of interest (ROI) within the imaged objectby the standard deviation (SD) of the signal in an ROIoutside the object (2–4). This method is valid for con-ventional single or multi-channel coil imaging recon-structed by a sum-of-squares algorithm, where noise isdistributed uniformly in the whole image. However, lin-ear combination of multi-channel coil acquisitionsbased on coil sensitivity maps (5) and widely used par-allel imaging acceleration techniques (6–8) cause aspatial variation in noise. Noise measured in oneregion of the image may, therefore, not necessarily rep-resent the noise elsewhere in that same image (9).

One of the most accurate definitions of SNR is basedon repetitive acquisitions of data under the same exactconditions at multiple time points. This method isreferred to as SNRmult, where SNR of each pixel is thendefined as the ratio between the mean and the SD of thesignal intensity time course of that pixel (9,10). When avery large number of time points are used, SNRmult rep-resents the true variation of the signal at a particularvoxel and should be considered the gold standard fornoise measurements. Another method described in theliterature is based on just two identical acquisitions,which are either averaged or subtracted to determinesignal or noise respectively (4,10). Both methods aregenerally not practical for in vivo measurements due toprolonged scanning time associated with repeated

1Department of Biomedical Engineering, Johns Hopkins University,Baltimore, Maryland, USA.2Russell H. Morgan Department of Radiology, Division of MagneticResonance Research, Johns Hopkins University, Baltimore, Maryland,USA.3Department of Radiology, Centre Hospitalier Universitaire Vaudoisand University of Lausanne and Center for Biomedical Imaging (CIBM),Lausanne, Switzerland.4Philips Healthcare, Cleveland, Ohio, USA.

Contract grant sponsor: NIH RO1; Contract grant numbers:HL084186, HL084186-04S1.

*Address reprint requests to: M.S., Johns Hopkins University MedicalSchool, Department of Radiology, 600 N. Wolfe Street, Park Bldg.Room 326, Baltimore, MD, 21287. E-mail: michael.schar@gmail.com

Received April 16, 2010; Accepted February 14, 2011.

DOI 10.1002/jmri.22571View this article online at wileyonlinelibrary.com.

JOURNAL OF MAGNETIC RESONANCE IMAGING 33:1330–1340 (2011)

CME

VC 2011 Wiley-Liss, Inc. 1330

acquisitions. Also they are susceptible to system driftand to image misregistration related to physiologicalmotion. Especially for 3D free breathing coronary MRangiography (MRA) in combination with parallel imaging(11,12), such an SNR quantification may be adverselyaffected by respiratory and cardiac motion (13). In addi-tion, repeated acquisitions of 3D coronary MRA data invivo for SNR quantification are impractical due to pro-hibitively long scanning time.

As alternatives to multiple acquisitions, two methodshave recently been proposed to measure SNR by recon-structing the image in SNR units directly (14) or by simu-lating repetitions of noise only images (15). However, bothtechniques suffer from a relatively high computationalburden. In addition, the direct SNR determination neces-sitates detailed knowledge of all image reconstructionsteps, which may not readily be available if image recon-struction is performed on a commercial MR system.

Hence, despite the availability of numerous andpowerful methods, there is no practical, general SNRmeasurement method available for coronary MRAacquired with parallel imaging. An SNR quantificationmethod that enables both the signal and the noise mea-surement at the exact same location is therefore needed.

For these reasons, an alternative, practical, andeasy-to-use SNR quantification method has beenimplemented for coronary MRA and follows the recom-mendations of the National Electrical ManufacturersAssociation (NEMA) (4). This new approach, which cur-rently comes at the expense of 30 s of additional scan-ning time only, has been implemented on a commercialMR scanner. Subsequently, the method’s validity andsuitability for quantitative coronary MRA SNR analysishave been investigated both in vitro and in vivo.

MATERIALS AND METHODS

Theory

An SNR measurement method recommended byNEMA (4) is based on the acquisition of a magnitudeimage and a second acquisition with identical settingsbut no radiofrequency (RF) pulses to obtain a purenoise image. Although this method has been known foryears, to the best of our knowledge, there is limited lit-erature investigating its performance and utility forMRI. Furthermore, a noise scan, which usually takesas long as the corresponding magnitude image acquisi-tion, would not only double the scanning time but alsosignificantly reduce overall practicality. For these rea-sons, this work will show that the duration of the noisescan can be abbreviated by an order of magnitude. Thefast noise acquisitions could significantly increase thesimplicity of SNR measurements in scans obtainedwith parallel imaging. In the following, we will refer tothe SNR-based on this noise scan as SNRnoRF.

The primary origin of random fluctuation in MRIsignals is thermal noise. RF receiver thermal noise inMRI systems (16) can be determined according to:

s2thermal / 4kT � Reff � BW ; ½1�

where s2thermal is the variance of noise voltage, k is the

Boltzmann constant, T is the resistor’s absolute tem-

perature, Reff is the effective resistance of the coil loadedby the body, and the BW is the bandwidth of the noise-voltage detecting system. Equation [1] indicates thatdata acquisitions with and without RF excitations havethe same thermal noise variance—provided that coilloading and receiver bandwidth are identical.

To measure noise, a fast noise acquisition schemehas been developed in the framework of a segmentedk-space spoiled gradient echo imaging sequence (17)(Fig. 1). The conventional or ‘‘anatomical’’ scan isrepeated with all the RF pulses and magnetic fieldgradient disabled (¼noise scan). Furthermore, trigger-ing to the R-wave of the electrocardiogram (ECG) isnot used. The respiratory navigator, which is per-formed with both RF pulse and gradient disabled, isset to accept all data for reconstruction. Cardiac andrespiratory motion during the noise scan acquisitionare assumed to have little effect on the measurednoise statistics because loading of the small phasedarray coil elements, and thus Reff, is dominated by thechest, which is considered stationary relative to thecoil. With this approach, the duration of noise scan isgreatly abbreviated while the thermal noise statisticsremain unaffected. It is important to note that bothanatomical and noise scans have identical geometry,receiver gain, and reconstruction algorithm (Thereconstruction algorithm should only include linearfilters. Nonlinear filters including image-based filtersmay affect the statistics of the anatomical and noisescan differently and thus-derived SNR values may nolonger be valid.). After completion of the scan, boththe anatomical dataset and the corresponding noisedataset are automatically reconstructed.

On the anatomical images, ROIs are selected for sig-nal measurements and these ROIs are automaticallycopied to the identical three-dimensional (3D) locationin the corresponding noise images. The signal (SnoRF)is defined as the average of the signal from the ROI inthe anatomical image while the noise (NnoRF) is pro-portional to the standard deviation of the signal foundin the equivalent ROI in the noise scan:

SnoRF ¼ meanr2ROI

ðSðrÞÞ;

NnoRF ¼ffiffiffiffiffiffiffiffiffiffiffiffiffi2

4� p

r� SDr2ROI

ðNðrÞÞ; ½2�

where S(r) is the anatomical image intensity in pixelr ¼ (rx, ry, rz), N(r) is the noise image intensity in pixelr. The coefficient H(2/(4-p)) accounts for the Rayleighdistribution of the noise in the magnitude image (2).This coefficient is different in the above-mentionedsum-of-squares reconstruction (18). The SNRnoRF isthus obtained as:

SNRnoRF ¼ SnoRF=NnoRF: ½3�

Based on an error propagation calculation similarto that in the Appendix in reference 10, the error onestimates of the SNR (¼sSNR) is proportional to1/HnROI in presence of homogenous noise in thatROI, where nROI is the sample size (number of inde-pendent pixels) in that ROI.

SNR Quantification with Parallel Imaging 1331

Hardware

All phantom and in vivo studies were performed on acommercial whole body 3.0 Tesla (T) MR scanner(Achieva R2.1, Philips Healthcare, Best, The Nether-lands) equipped with a six-element cardiac phased-array coil for signal reception and vector-ECG (19)triggering. Parallel imaging was performed using sen-sitivity encoding (SENSE) (7).

Phantom Studies

Phantom experiments were performed to validateSNRnoRF in comparison to SNRmult. First, noise mapsfor different acceleration factors were generated toshow spatial variations as a qualitative comparison.Then, SNR maps were used in a quantitative compari-son considering various acquisition and measurementparameters.

Image Acquisition

First, a multislice survey scan was obtained in axial,sagittal, and coronal views to identify the location of acylindrical fluid phantom. This was followed by aSENSE reference scan with a spatial resolution of 3.0� 3.0 � 4.0 mm3. Then, a 2D segmented k-spacespoiled gradient echo imaging sequence with centrick-space profile ordering was applied to acquire a 3-mm-thick coronal slice with a field-of-view (FOV) of256 � 256 mm2 and an acquired matrix size of 128 �128. The phase encoding direction was left–right (LR)

and imaging was performed with artificial ECG trig-gering (RR interval ¼ 800 ms). The pulse sequencehad 12 RF excitations per cardiac cycle, a repetitiontime (TR) of 5.2 ms and an echo time (TE) of 2.6 ms.No fractional echo signal-readout was used and theBW was 383.2 Hz/pixel, which remained unchangedfor all phantom data acquisitions. The image acquisi-tion was repeated 63 times (for SNRmult) consecutivelyand paused for 5 s, to ensure that all signal hasdecayed, before the fast noise image acquisition (forSNRnoRF) started. To investigate the influence of dif-ferent levels of signal, scans with RF excitation anglesof 20� and 8� were performed. For both experiments(20� and 8� RF excitation), SENSE acceleration factorsranging from 1 to 5 were applied in the LR direction.This resulted in a total of 10 individual scans each ofwhich contained 63 anatomical and one noise image.

ROI Size

A small ROI (ROIsmall) of 10 � 10 pixels was selectedon the images. To assess the relationship betweenROI size and SNR measurement, the SNR measure-ments were repeated with a larger ROI (ROIlarge) of 20� 20 pixels to ensure that more independent sampleswere included in the analysis.

SNR Measurement Methods

Based on the magnitude image data provided by theMRI system, SNR was measured using SNRmult andSNRnoRF in MATLAB (MATLAB R14, The MathWorks

Figure 1. Schematic of the pulse sequence: The anatomical scan consists of a conventional 3D coronary MRA sequence. Thesegmented k-space spoiled gradient echo (GRE) data acquisition (ACQ), starting at the predetermined trigger delay (Td) afterthe R-wave, is preceded by the magnetization preparation pulses including a T2prep pulse, a pencil-beam respiratory naviga-tor pulse (NAV), a fat saturation pulse (FatSat) and a spatially selective saturation pulse (SatSlab). In the noise scan, however,data acquisition ACQ is executed without ECG triggering, RF excitations or gradient (Gm, Gp, Gs) pulses. Magnetization pre-pulses are omitted except NAV and FatSat, although their RF and GR are disabled as well. The modules as delineated bysquare brackets are repeated n times. By using shorter modules without ECG triggering or respiratory gating, the duration ofthe noise scan can be greatly shortened compared with the anatomical scan.

1332 Yu et al.

Inc., Natick, MA). SNRmult was calculated from repeti-tions 4 to 63 to avoid transient effects before steady-state of the magnetization was reached. Linear correc-tion was applied to the signal intensity of repetitions4–63 to compensate for residual intensity drift duringthe acquisition. The signal of each pixel (cmult) wasdetermined as the average of the pixel intensity fromtemporal repetitions, while the noise of each pixel(smult) was determined as the SD of the pixel intensityseries. SNRmult of a user-specified ROI was the quo-tient of average signal (Smult) over average noise (Nmult)among all the pixels in the ROI, as:

CmultðrÞ ¼ meank¼4;���;63

ðSkðrÞÞ;Smult ¼ mean

r2ROIðCmultðrÞÞ;

smultðrÞ ¼ SDk¼4;���;63

ðSkðrÞÞ;Nmult ¼ mean

r2ROIðsmultðrÞÞ;

SNRmult ¼ Smult=Nmult ;

½4�

where Sk(r) is the anatomical image pixel intensity ofthe kth repetition (9).

SNRnoRF was calculated from the 10th repetition(steady state) of the anatomical scan and the noisefrom the noise scan (64th repetition) as described inEqs. [2] and [3].

Spatial Variation of Noise

The spatial variation of noise and its dependence onSENSE acceleration factors R was analyzed. To gener-ate noise maps, the noise of each pixel was calculatedfrom a ROIsmall centered at the targeted pixel. Noisemaps based on the noise statistics NnoRF (Eq. [2]),Nmult, and smult (Eq. [4]) were generated for data setsacquired with different R and an RF excitation angleof 20�. A comparison between NnoRF and smult wasmade by computing |NnoRF � smult|.

Quantitative Validation of SNRnoRF

SNR maps for SNRnoRF and SNRmult were generatedfor a rectangular area in the center of the imagedphantom (rectangle in Fig. 2a). The SNR in each pixelwas calculated from a square shaped ROI centered atthe targeted pixel. SNR measurements were per-formed for all possible 10 � 10 and 20 � 20 ROIswithin the rectangle (20). For a quantitative valida-tion, the relative differences between the proposedSNRnoRF and the reference standard SNRmult, i.e.,|SNRnoRF � SNRmult| / SNRmult, was calculated for allpixels in the rectangular area. The size of the rectan-gle was 60 � 54 on the images. The average andstandard deviation of the relative differences over thearea were reported as a scalar measure that describesthe quality of the SNR measurement method.

In addition, five locations, on the left, right, center,top, and bottom of the image (circles in Fig. 2b), wereselected. Their SNR values for all the RF excitationangles, ROI sizes and five locations in the image, werecomputed as a function of the different SENSE accel-

eration factors R and linear least-squares fitting wasperformed with SNRmult on the x-axis versus SNRnoRF

on the y-axis.

G-Factor

G-factor maps based on the acquired SENSE referencescan can be generated by the standard MRI systemusing the coil sensitivity map. Alternatively, the g-fac-tor can be determined according to the definition (7):

gðRÞ ¼ SNR1ffiffiffiffiR

p � SNRR

: ½5�

Hereby, SNR1 refers to the SNR on images acquiredwith a SENSE factor of R ¼ 1, and SNRR to that withR > 1.

G-factor maps calculated by the MRI system wereexported and taken as the reference standard in thefollowing g-factor comparison. The g-factor mapsaccording to Eq. [5] were also generated from theSNRnoRF data with an RF excitation angle of 20� andwith ROIsmall. For each SENSE acceleration factor, theaverage g-factor and one standard deviation over therectangular area (Fig. 2a) were computed for bothg-factor maps reconstructed by MRI system and cal-culated based on SNRnoRF.

In Vivo Studies

For coronary MRA, SNRmult cannot be performed dueto time constraints. Instead, to further demonstratethe ability of SNRnoRF to measure local SNR in vivo,we hypothesized that the signal ratio between myocar-dium and chest muscle is different from the SNR ratiobetween the two. At 3T, chest muscle has a T1 of1420 ms (21) and a T2 of 32 ms (21), while myocar-dium has a T1of 1220 ms (22) and a T2 of 59 ms (23).Therefore, and after T2-preparation, which generatesT2 weighted image contrast (24,25), the signal of thechest muscle with the shorter T2 is expected to besmaller than that of the myocardium with the longerT2. When applying the uniform sensitivity reconstruc-tion (5,7), the signal of each tissue and thus the rela-tive signal depend only on the muscle tissue proper-ties such as proton density, T1, T2, but not on coil

Figure 2. a: The relative difference between SNRnoRF andSNRmult was averaged over pixels within the depicted box.The box has a size of 60 � 54 pixels on the image. b: SNRmeasurements from five locations (centered in the circles)were used for the linear regression between SNRnoRF andSNRmult.

SNR Quantification with Parallel Imaging 1333

sensitivity. However, the local noise does depend on(among other factors) coil sensitivity, i.e., on whetherthe ROI is located close to or more distant from thereceive coils. Accordingly, in the case of spatially het-erogeneous noise, the SNR ratio at two locationswould differ from the signal ratio because SNR isdetermined by both signal and local noise.

Coronary MRA data obtained in 10 healthy adultsubjects (26) were analyzed. The study protocol wasapproved by our Institutional Review Board and allsubjects gave written informed consent to participate.For each subject, two 3D segmented k-space spoiledgradient echo acquisitions of the right coronary artery(RCA) with identical scan times and acquisition win-dows of 40 ms, but different SENSE acceleration fac-tors (1 and 2), TR (3.3 and 6.6 ms), TE (1.2 and 1.8ms), RF excitation number (12 and 6), and readoutBW (724.1 and 149.3 Hz/pixel) were obtained. Thethree-dimensional fast noise scans always followedthe anatomical scan immediately after a 5 s pause.

The ‘‘Soap-Bubble’’ coronary analysis tool asdescribed by Etienne et al. (27) was extended with theability to quantify SNRnoRF. Rectangular ROIs weremanually drawn on the anatomical images in the leftventricular wall and in the posterior chest wall,respectively, where signal and SNR of myocardiumand skeletal muscle were calculated based on Eqs. [2]and [3]. In one representative coronary MRA dataset,the SNR map was calculated by a sliding ROI of 10 �10 pixels size and for all the pixels in the slice.

All results are reported as mean 6 1 SD among allthe subjects. For each SENSE acceleration factor, sta-tistical tests were performed to compare the signal ofmyocardium and that of skeletal muscle, using apaired two tailed Student’s t-test, with a P-value <0.05 representing significant difference. The same sta-tistical test was applied to SNR of myocardium andskeletal muscle. The above-described SNR ratio andsignal ratio were calculated on all in vivo human data-

sets. Then, the SNR ratio was further compared withthe signal ratio by using a paired two tailed Student’st-test, with a P-value <0.05 representing significantdifference.

RESULTS

Phantom Studies

Figure 3 shows representative magnitude images ofanatomical scans and the corresponding noise scans(no RF) at various SENSE acceleration factors. Withhigher SENSE factors, the intensity of noise increasesas SNR decreases in the anatomical images. Consist-ent with earlier findings of others (7), structuredregions of high noise are seen centrally and moreprominently as the SENSE acceleration factorincreases. In addition, the spatial coherence visible onthe noise images in the lower row is in good agree-ment with the artifacts seen on the anatomical imagesin the upper row.

The noise statistics smult, Nmult, and NnoRF are dis-played as pseudo color images in Figure 4. NnoRF dem-onstrates similar spatial distribution and magnitudeof noise statistics as Nmult, which corresponds to aspatial average of smult. By subtracting NnoRF fromsmult, the coherent structures shown in smult arelargely removed and a minor residual difference signalremains at the edges of these structures due to thelower spatial resolution of the NnoRF image. The differ-ence between NnoRF and smult is one order of magni-tude lower than the measured noise levels. It isnoticed that, for an acceleration factor R larger than2, NnoRF differs considerably from smult in backgroundareas outside of the object. The image reconstructionat these locations in background areas is unpredict-able due to the absence of coil sensitivity in theSENSE reference scan, and thus the noise quantifica-tion in the background is not recommended.

Figure 3. Phantom images (row a) and noise images (row b) when SENSE acceleration factors R ¼ 1, 2, 3, 4, 5 were applied.All the images were acquired with an RF excitation angle of 20�. All phantom images are displayed with an identical windowlevel, while the noise images with individually adapted window levels. The minimal and maximal intensities in each windowlevel are labeled under the corresponding image.

1334 Yu et al.

Quantitative results in Figure 5 represent the aver-age relative differences between SNRnoRF and the ref-erence standard SNRmult as a function of ROI size andthe RF excitation angle. These data are shown foracceleration factors R ranging from 1 to 5. The aver-age relative differences for SENSE acceleration factorsfrom 1 to 4 are below 10.1%. In contrast, SNRnoRF

measurements obtained at a SENSE acceleration fac-tor of 5 may differ up to 15% relative to the referencestandard SNRmult. Comparing RF excitation angles of8� and 20�, the relative difference increased slightlyfor some SENSE acceleration factors but decreasedfor others. Therefore, the choice of the RF excitationangle, and thus the absolute signal level, does notseem to have a major effect on the SNR measurementusing SNRnoRF. However, and as expected, the ROIsize is a major determinant for differences betweenSNRmult and SNRnoRF. ROIs of larger size help toreduce the error of SNRnoRF relative to the SNRmult

method for SENSE acceleration factors ranging from 1

to 4, although increasing ROI size decreases sensitiv-ity to spatial variation.

Linear regressions demonstrate a high correlationbetween SNRnoRF and SNRmult (Fig. 6). For eachSENSE acceleration factor, SNR values of five selectedlocations from two different RF excitation angles andtwo ROI sizes are combined. These dots cluster intotwo separate SNR ranges on the plots because two dif-ferent RF excitation angles (8� and 20�) were used forimage acquisition. R2 is above 0.93 for all SENSEacceleration factors. The slopes in the linear regres-sion function with SENSE acceleration factors rangingfrom 1 to 4 are close to 1 (1.13, 1.02, 0.96, and 1.03for R ¼ 1, 2, 3, and 4, respectively), and the interceptsare small. The linear regression reflects that SNRnoRF

has negligible systematic bias compared with SNRmult.However, with a SENSE acceleration factor of 5, theslope is 0.72, which indicates that SNRnoRF mayunderestimate the ‘‘true’’ SNR at higher accelerationfactors. The average g-factors (Table 1) that are

Figure 4. Spatial noise in phantom study calculated by smult (row a), Nmult (row b), and NnoRF (row c) at five SENSE accelera-tion factors (R ¼ 1, 2, 3, 4, 5) respectively. smult, Nmult, and NnoRF (rows a–c) showed structured regions of high noise centrallyand more prominently as the acceleration factor increases. The absolute difference |NnoRF - smult | is displayed in row d, onwhich edges are still seen, but the magnitude of absolute difference is reduced. For all images the phase encoding directionwas oriented left–right, RF excitation angle was 20�, and the window level is identical. ROI size of 10 � 10 was used in Nmult

and NnoRF computation.

SNR Quantification with Parallel Imaging 1335

calculated based on SNRnoRF agree well with thosegenerated by the MRI system. The average g-factorsare indicators of noise inhomogeneity over the image,and the SD of g-factors reflect that the g-factors arespatially varying.

In Vivo Studies

The acquisition of the 3D volumetric noise image wascompleted in 30 s only, while no ECG triggering,breathholds, or navigators for respiratory motion sup-pression were needed. Representative anatomical andnoise images, acquired with a SENSE factor of 2, andthe corresponding SNR map are shown in Figure 7.Noise amplification (Fig. 7b) is observed in the centerof the body and in cranial direction consistent withregions with reduced coil sensitivity. In this represen-tative example, the ROI localized in the left ventricularmyocardium is in an area with an increased noiselevel (Fig. 7, solid arrow). Conversely, the ROI local-ized in posterior skeletal muscle represents an areacloser to the surface coil with a reduced noise level(Fig. 7, dashed arrow). Quantitative measurementsshow that the signal of myocardium is significantlyhigher than that of skeletal muscle (for R ¼ 1: 161.36 30.6 versus 121.7 6 25.5, P < 0.05; for R ¼ 2:165.9 6 35.2 versus 117.1 6 16.4, P < 0.05), butsimultaneously, the SNR of myocardium is signifi-cantly lower than that of skeletal muscle (for R ¼ 1:12.3 6 2.5 versus 15.4 6 3.8, P < 0.05; for R ¼ 2:17.0 6 3.8 versus 22.6 6 4.8, P < 0.05). Statistical

tests also show that the SNR ratio is significantlysmaller than the signal ratio (for R ¼ 1: 0.81 6 0.11versus 1.34 6 0.20, P < 0.05; for R ¼ 2: 0.75 6 0.10versus 1.42 6 0.18, P < 0.05; both are SNR ratio ver-sus signal ratio).

DISCUSSION

In this work, we have described a fast and easy-to-use method for quantifying SNR on coronary MRAimages acquired with SENSE acceleration. This fastSNRnoRF method has been characterized and validatedin phantom studies in comparison to a referencestandard method SNRmult. Good agreement of meas-ured noise statistics and SNR behavior between thetwo methods was observed both qualitatively andquantitatively. The capability of SNRnoRF in measuringspatially dependent SNR was also demonstrated within vivo studies.

The SNRnoRF method consists of a noise image thatis acquired without RF pulses and magnetic field gra-dients. This is enabled by the linearity of parallelimaging reconstruction methods. As a result, thereconstruction process can be regarded as an opera-tor that acts on both signal and noise separately (15).A noise image acquired with SNRnoRF offers several re-markable advantages when compared with a noiseimage that is obtained through the acquisition of se-rial identical anatomical images. First, the noise scancan be acquired orders of magnitude faster, whichmakes it perfectly well suited for lengthy volumetriccoronary MRA scans. In practice, a noise scan can becompleted within 30 s for a 3D coronary MRA scanthat takes 10 min to acquire. In the current imple-mentation, one order of magnitude faster scan dura-tion was achieved by removing most of the magnetiza-tion preparation pulses and the waiting periodbetween the acquisition windows. However, duringeach TR, only the time for signal sampling is theoreti-cally required to fill the noise k-space. This suggeststhat the 30-s noise scan may be further abbreviatedto 4 s only. Second, without MR signal from theobject, the noise images are free from artifactsinduced by motion or physiological fluctuation. Thisimportant feature permits SNRnoRF to be computed forquantitative cardiac and time resolved contrastenhanced imaging, which cannot easily be performedusing the multiple acquisitions method. The SNR foreach repetition of the anatomical scan is determinedby the signal measured in that repetition and thenoise extracted from the noise scan. Should the ana-tomical scan require breathholding as a mechanismto suppress respiratory motion artifacts, the breath-hold duration does not have to be prolonged by theacquisition of the noise scan because it may beacquired during free breathing as long as the coilloading remains similar. Moreover, the SNRmult

method may be adversely affected by misregistrationoriginating from object motion during the time courseof data acquisition. This can be avoided with theSNRnoRF technique because a noise image is no longercontaminated by motion artifacts. In addition, the

Figure 5. The average relative differences between SNRmult

and SNRnoRF (|SNRnoRF-SNRmult|/SNRmult) as a function ofSENSE acceleration factor (R) in the phantom study. The av-erage and SD (error bars) are determined among voxelswithin the center area on the image (rectangle shown in Fig.2a). The horizontal dashed line shows a relative differencelevel of 10%. Panel a shows data acquired with an RF excita-tion flip angle (FA) of 20�, whereas the data in panel b wereacquired with a FA of 8�.

1336 Yu et al.

noise acquisition comes at no extra costs such as pre-paratory steps, extra setup time, or offline processing.Finally, measurement of contrast-to-noise ratio (CNR)is based on local signal and noise measurements, andtherefore can be obtained conveniently in the same

manner as SNRnoRF. All these favorable properties maymake the SNRnoRF method useful to be adopted in rou-tine clinical scanning where quantitative analyses orsystematic protocol optimization steps, and quantita-tive end-points related to image quality are essential.

Figure 6. Scatter plot of SNRmult versus SNRnoRF measured in the phantom study at different SENSE acceleration factors.SNRmult and SNRnoRF were measured in five pixels within the phantom (Fig 2b). The least squares fit of linear functions andthe corresponding R2 are shown on the scatter plot. Each plot has its axis scales adjusted to SNR ranges at individual SENSEacceleration factors.

SNR Quantification with Parallel Imaging 1337

An assumption underlying SNRnoRF is that all pixelsin the user selected ROI have the same statisticalnoise distribution. SENSE reconstruction leads to in-homogeneous noise across the image. BecauseSNRnoRF is a ROI-based measurement, its sensitivityto spatial variations is reduced when compared withSNRmult. However, the noise statistics change slowlyas a function of the location and can be consideredregionally homogeneous as long as the g-factorremains low. In our phantom study, mean g-factorswere lower than 2 and their standard deviation wereless than 0.5 as long as the SENSE acceleration factorremained below 5 (see Table 1) with the current coilsetup. For these moderate acceleration factors, theaverage relative deviations of SNRnoRF from SNRmult arebelow 10.1% (see Fig. 5). However, when the SENSEacceleration factor is 5, more coherent geometricalstructures of noise amplification were observed. Thesemight be responsible for the relatively sharp increasein relative SNR deviations for higher R values, espe-cially if larger ROIs are used. In practice, adequateSENSE acceleration factors are usually chosen whichare well supported by the coil arrangement. A g-factorbeyond 2 is most commonly avoided because severeimage degradation due to incomplete SENSE unfold-ing may occur. Therefore, over a reasonable range ofg-factors and SENSE acceleration factors, the SNRnoRF

method is reliable and fast for the quantification ofSNR from homogeneous regions.

The ROI position and size should also be consideredto ensure that the noise distribution in the ROI is suf-ficiently homogeneous. ROI positions in areas of foldover, or other kinds of artifacts on the anatomicalimage should be avoided. In practice, the ROI size isalso limited by the homogeneity of the target area onthe anatomical image and the noise statistics at thatsame location. In homogeneous regions, larger ROIsizes contribute to measurement precision, becausethe error in NnoRF is proportional to 1/H nROI, wherenROI is the number of independent pixels in the ROI.With SENSE acceleration factors 1 to 4, noise amplifi-cation and local variation are moderate. Thus enlarg-ing ROI and including more samples contribute toreduce the relative error of SNRnoRF relative to theSNRmult method. Our studies have demonstrated thatthe SNRnoRF method performed consistently well overa range of SNR levels.

In general, all previous knowledge about ROI-basedSNR measurement can be readily applied with theSNRnoRF method. For example, the magnitude biascorrection can be applied to reduce the overall error ofthe signal estimation at low SNR (28).

Our measurements in vivo confirm that SNRnoRF iswell-suited to measure spatially dependent SNR onMR images acquired with SENSE. The relative signalsobtained in our study show that the myocardium has�30–40% higher signal intensity than skeletal muscle.These results agree well with values in normal sub-jects in the literature (29–31) and may be attributableto shorter T2 that has been reported of skeletal mus-cle. However, the noise power in the myocardiumwhich is located more distant from the signal receivesurface coils is elevated compared with the noise inthe skeletal muscle which is much closer to the coils(Fig. 7). Therefore, despite the higher signal intensityof myocardium, the SNR of myocardium is reducedwhen compared with skeletal muscle. One may noticethat SNR obtained with a SENSE acceleration factorof 2 is higher than that with factor of 1 for both car-diac and skeletal muscles. As previously reported,this is attributable to a longer TR, a lower receiverbandwidth and an improved RF transmit to receive

Table 1

Comparison of g-Factors Obtained by Coil Sensitivity Profile and

SNRnoRF*

SENSE acceleration factor Coil sensitivity No RF

R ¼ 2 1.06 6 0.08 1.04 6 0.12

R ¼ 3 1.21 6 0.15 1.14 6 0.17

R ¼ 4 1.90 6 0.43 1.64 6 0.25

R ¼ 5 4.57 6 1.61 4.78 6 1.08

*All the g-maps were from data acquired with an RF excitation

angle of 20�. For SNRnoRF, ROI size of 10�10 was used to calcu-

late the g-factor. The average and standard deviation were meas-

ured within the center area of 60 � 54 pixels in the g-map.

Figure 7. One slice of anatomical (a) and noise (b) image from the representative in vivo 3D volumetric coronary MRA, whichwas acquired with a SENSE acceleration factor of 2. The myocardium ROI (solid arrow) and skeletal muscle ROI (dashedarrow) are located at identical position on the anatomical and noise image. The SNR map (c) of the slice was generated usinga moving ROI of 10 � 10 for illustration only. The minimal and maximal intensities in each window level are labeled underthe corresponding image.

1338 Yu et al.

duty cycle used in the sequence with a SENSE accel-eration factor of 2 (26,32).

In the current study, experiments were performedwith a specific coil, pulse sequence and parallel imag-ing technique. However, by compacting the recon-struction processes into a ‘‘black box’’ as available onmost commercial MRI systems, the SNRnoRF method isexpected to be applicable with other coils, signalacquisition techniques, k-space sampling schemes ortrajectories, image reconstruction methods, and linearprocessing associated with coronary MRA. Therefore,the combination with balanced steady state free pre-cession (bSSFP) (12) or spin echo pulse sequences(33) seems straightforward but remains to beexplored. For parallel imaging approaches that rely oncalibrating k-space lines that are acquired along withthe normal image acquisition, such as generalizedautocalibrating partially parallel acquisitions(GRAPPA) (8) and modified SENSE (34) reconstruc-tion, the current method may not directly be appliedand modifications of the reconstruction algorithmmay be needed. However, if the ‘‘black-box’’ containsany nonlinear filtering, which may violate the con-dition of identical reconstruction for both the anatom-ical and the noise image, the proposed techniqueshould not be used.

In conclusion, the SNRnoRF method demonstratedhere is a practical and easy-to-use method to quantifySNR on coronary MRA when parallel imaging is used.It allows SNR measurement in any user specified ROIon the image with very little extra cost in scanningtime and no extra off-line image processing or analy-sis is required. The proposed method is also not jeop-ardized by misregistration in contrast to thoseapproaches that depend on repeated image acquisi-tions. One limitation of SNRnoRF, like any other ROI-based measurement, is its reduced sensitivity to spa-tial variation of noise when compared with the goldstandard SNRmult. SNRnoRF quantification may not bewell-suited for high acceleration factors and nonlinearfilters during reconstruction or post processing. Ingeneral, the proposed methodology will provide a use-ful tool for objective and quantitative evaluation ofcoronary MRA acquired with different pulse sequen-ces, MRI platforms, coil arrays, and reconstructionmethods and may also find applications outside ofcoronary imaging.

ACKNOWLEDGMENTS

The authors thank Prof Daniel Herzka (Johns Hop-kins University) for providing constructive commentson this manuscript, Marc Kouwenhoven and JoukeSmink (Philips Healthcare, Best, the Netherlands) forhelpful discussions.

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