High-Pass GRAPPA: An Image Support ReductionTechnique for Improved Partially Parallel Imaging

Feng Huang,* Yu Li, Sathya Vijayakumar, Sarah Hertel, and George R. Duensing

Partially parallel imaging (PPI) is a widely used technique inclinical applications. A limitation of this technique is the strongnoise and artifact in the reconstructed images when high re-duction factors are used. This work aims to increase the clinicalapplicability of PPI by improving its performance at high reduc-tion factors. A new concept, image support reduction, is intro-duced. A systematic filter-design approach for image supportreduction is proposed. This approach shows more advantageswhen used with an important existing PPI technique, GRAPPA.An improved GRAPPA method, high-pass GRAPPA (hp-GRAPPA), was developed based on this approach. The newtechnique does not involve changing the original GRAPPA ker-nel and performs reconstruction in almost the same amount oftime. Experimentally, it is demonstrated that the reconstructedimages using hp-GRAPPA have much lower noise/artifact levelthan those reconstructed using GRAPPA. Magn Reson Med59:642–649, 2008. © 2008 Wiley-Liss, Inc.

Key words: GRAPPA; image support; parallel imaging; high-pass filter

Partially parallel imaging (PPI) techniques have been usedroutinely in clinical applications to reduce acquisitiontime or motion artifacts. However, PPI techniques havesome intrinsic problems. For example, images recon-structed by SENSE (1) have errors caused by g-factor andinaccurate sensitivity maps; images reconstructed byGRAPPA (2) have errors caused by imperfect reconstruc-tion convolution kernels. These errors manifest them-selves either as exaggerated noise or as residual aliasingartifacts and they can significantly reduce the diagnosticquality of the image when the acceleration factor goeshigh. To reduce the noise level and residual aliasing inclinical reconstruction, the acceleration factor has to berestricted to values far lower than the theoretically achiev-able limit (e.g., for most clinical purposes, the accelerationfactor is around 2 for an 8-channel head coil). The purposeof this work is to provide a simple approach to moderatethis restriction. The proposed method is based on theobservation that PPI techniques perform better on imageswith smaller support. Mathematically, the support of afunction is the closure of subsets of the domain of defini-tion, on which the function assumes a nonzero value. Inreality, the intensity value of any MR image pixel is non-zero because of noise. In this article the concept of “zero”regions is used to describe the regions that have very lowintensity. Image support is defined as the “nonzero” re-

gions. Even though this concept of “zero” regions veersfrom the strict definition, the descriptive concept offers asimple way to understand the mechanism of the proposedtechnique in this article.

The reason for better PPI performance on an image withsmall support can be explained in image space as follows.When a set of MRI data is acquired with acceleration, thenumber of phase encoding (PE) lines in k-space is reducedand the direct fast Fourier transform (FFT) of the down-sampled data generates overlapped images. The number ofoverlapping layers, i.e., superimposed pixels, equals theacceleration factor. If a superimposed pixel contains lay-er(s) from “zero” regions (the intensity is close to zero inreality), the intensity of “zero-layers” can be set to 0 with-out generating considerable errors in the reconstructedimage. If the locations of these “zero” intensity overlap-ping layers are known, then only the nonzero overlappinglayers need unfolding. For an image with small imagesupport, the number of nonzero overlapping layers ofmany superimposed pixels is less than that of an imagewith large image support, which means fewer unknownsin the unfolding equations (e.g., in the SENSE reconstruc-tion equations). Hence, the unfolding process would beeasier for images with smaller image support.

In a real MRI experiment the image support is alwaysdependent on the imaging subject and it cannot be physi-cally changed. However, it can be artificially reduced be-fore unfolding and recovered after unfolding for PPI. Thereare several approaches to achieve this goal. One straight-forward approach is to increase the field of view (FOV)during acquisition. However, this technique may eitherincrease acquisition time or reduce spatial resolution. Indynamic imaging, different time frames often have greatsimilarity. The invariant component of these images canbe reconstructed separately and subtracted from each timeframe to reduce its image support. k-t GRAPPA (3) imple-ments this idea in k-space. Encouraging results have beenreported (3,4) for dynamic imaging using image supportreduction techniques. However, this approach is applica-ble only to dynamic imaging applications with significantsimilarities between time frames. For static imaging ordynamic imaging with reduced similarity between timeframes, the development of other image support reductionapproaches is necessary. If one notices that the main com-ponent of signals in image support is low-frequency infor-mation, it can be understood that image support can beefficiently reduced by suppressing low-frequency informa-tion with a high-pass filter. This method can be imple-mented in either image space (5) or in k-space (6). Xiang(5) and Chang and Xiang (7) demonstrated the benefits ofartificial image support reduction with or without parallelimaging techniques.

*Correspondence to: Feng Huang, Advanced Concept Development, InvivoCorp., 3545 SW 47th Ave., Gainesville, FL 32608.E-mail: fhuang@invivocorp.comReceived 9 May 2007; revised 18 September 2007; accepted 30 October2007.DOI 10.1002/mrm.21495Published online 24 January 2008 in Wiley InterScience (www.interscience.wiley.com).

Magnetic Resonance in Medicine 59:642–649 (2008)

© 2008 Wiley-Liss, Inc. 642

In this work the image support reduction concept isproposed and its effect in k-space is discussed. High-passfilters are designed to reduce image support. A method ofimplementing image support reduction with GRAPPA ispresented and its advantages are demonstrated. Both sim-ulated and in vivo data are used to demonstrate the advan-tages of image support reduction technique for PPI.

THEORY

In this section, general concepts and methods are demon-strated using simulated data. A set of PPI data was gener-ated using the Shepp-Logan phantom and sensitivity mapsfrom a prototype 4-channel cardiac coil (Invivo, Gaines-ville, FL). Random noise was added during simulation.The matrix size of the simulated dataset was 256 � 256 �4. The PE direction was along the vertical direction in theimage. Full k-space data were simulated, but only partialk-space data were used for reconstruction. If one line isused out of every R lines, excluding the central autocali-bration signal (ACS) lines, then the acceleration factor is Rby definition. The central 64 lines of k-space data wereused as ACS lines. The net reduction factor is defined asthe ratio of the total number of PE lines to the number ofPE lines used for reconstruction (including the centralACS lines).

Concept of Image Support Reduction

Image support reduction can be descriptively defined asthe reduction of “nonzero” regions in an image, whichmainly consist of low-frequency information. It is wellknown that the low-frequency information of an image islocated at the center of its k-space. Hence, suppressing thecentral k-space data will reduce the image support. Thereduction of the number of nonzero overlapping layers inthe image generated with PPI data then follows. Withreduced aliasing the performance of PPI reconstruction isimproved. A simple method for image support reduction isproposed in SPEED (5) by using the differential operationin image space. In k-space the differential operation alongPE direction may be implemented as a high-pass filterdefined by:

F1�ky� � e�i2��ky/Ny� � 1, [1]

where ky is the count of PE lines. This filter is called filter1 in this work. Figure 1 shows the simulated phantombefore (Fig. 1a) and after (Fig. 1c) this filter. From Fig. 1c itcan be seen that the area of “nonzero” region is dramati-cally reduced after the filter. Also shown in this example,reduction of image support does not necessarily reduce thesize of the object; it generates more zeros in the FOV.Figure 1b,d shows the direct FFT of the partial k-spacedata at an acceleration factor 4 with the original (Fig. 1b)and filtered (Fig. 1d) data. Because of the reduction inimage support, aliasing is significantly reduced. It is ex-pected that the reconstruction from Fig. 1d to Fig. 1c iseasier than that from Fig. 1b to Fig. 1a. To compensate forthe image support reduction, i.e., reconstructing Fig. 1afrom Fig. 1c, the inverse of filter 1 needs to be applied toFig. 1c (5). Notice that filter 1 is 0 when ky is 0, and hence

this PE line can not be recovered by inverse filter andneeds to be replaced with the acquired data

hp-GRAPPA

With a set of PPI data after image support reduction, eitherSENSE or GRAPPA may be applied to perform the recon-struction. One implementation with SENSE is SPEED-ACE(7). Besides the complexity of calculation of sensitivitymaps, one concern for the use of SENSE is its requirementfor the explicit use of geometry information of the imagesupport. In comparison, GRAPPA avoids the explicit cal-culation of coil sensitivity profiles, and hence it is naturalto test if GRAPPA can take advantage of image supportreduction without the explicit use of geometry informationof image support. In Fig. 1 GRAPPA was applied to partialk-space data (R � 4, 64 ACS lines) with and without imagesupport reduction. The inverse filter and replacement ofcenter k-space lines with ACS were applied after GRAPPAto compensate for the reduced image support. Notice thatin this process no information of image support was ex-plicitly used; only a filter and its inverse were appliedbefore and after GRAPPA. Figure 1e (without image sup-port reduction) and 1f (with image support reduction)show the results. It is observed that GRAPPA generatedmuch better results with the filtered data even without anyknowledge of nonzero overlapping layers. Compared to

FIG. 1. Demonstration of image support reduction. a: The originalimage. c: Image with reduced image support by high-pass filtering.b,d: The wrapped image at acceleration factor 4 with the original (b)and filtered (d) data. e,f: Results of GRAPPA with original data (e)and filtered data (f).

High-Pass GRAPPA for Improved PPI 643

Fig. 1e, Fig. 1f has dramatically reduced noise/artifactlevel. This example demonstrates the capability ofGRAPPA to employ reduced image support without thenecessity to guess nonzero overlapping layers and testtheir locations.

Based on this observation, GRAPPA is proposed to im-plement parallel imaging with image support reduction.The partially acquired k-space data are processed with ahigh-pass filter (point-wise multiplication with the filter ink-space) and the resulting dataset corresponds to an imagewith reduced image support. The filtered ACS lines areused to calculate the corresponding convolution kernelsfor reconstruction. The output of GRAPPA is processed bythe inverse of that high-pass filter (point-wise division bythe high-pass filter) to generate the full k-space data cor-responding to the original image. Finally, the acquireddata are used to substitute the reconstructed k-space dataat the acquired k-space locations to generate the final out-put of k-space data. Since a high-pass filter is used toreduce the image support, this technique is called high-pass GRAPPA (hp-GRAPPA). Figure 2 demonstrates theprocedure of this technique. It can be seen in Fig. 2 that thereconstruction kernel is still obtained from the existingGRAPPA technique. Only one filter and its inverse areapplied before and after GRAPPA; the integration is easyand the reconstruction time of hp-GRAPPA is almost thesame as that of GRAPPA. Compared to SPEED-ACE, thisimplementation is simpler: there is no necessity to guessthe reduced number of nonzero overlapping layers and testtheir locations, or calculate coil sensitivity maps. Com-pared to the result of original GRAPPA (Fig. 1e), the resultof the proposed hp-GRAPPA technique (Fig. 1f) has signif-icantly reduced noise/artifact level.

MATERIALS AND METHODS

Data Acquisition

To compare GRAPPA and hp-GRAPPA at acceleration fac-tors of a broad range, a dataset acquired with a 32-channelcoil (Invivo, Gainesville, FL) was used. The cardiac func-tion dataset was collected on a 1.5T SIEMENS Avantosystem (Siemens Medical Solutions, Erlangen, Germany)using cine TrueFISP sequence (FOV 340 � 255 mm, matrixsize 192 � 150, TR 2.86 ms, TE 1.43 ms, flip angle 46°,slice thickness 6 mm, number of averages 1). PE directionwas anterior–posterior. To demonstrate the performance ofhp-GRAPPA for data acquired with a small number ofchannels, a dataset acquired with a 4-channel cardiac coilwas used. Sagittal cardiac images were acquired on a 1.5TGE system (GE Healthcare, Waukesha, WI) using a GE4-channel cardiac coil. A fast imaging sequence employingsteady-state acquisition (FIESTA) was used (FOV 280 mm,matrix size 192 � 224, TR 4.510 ms, TE 2.204 ms, flipangle 45°, slice thickness 6 mm, number of averages 2). PEdirection was anterior–posterior.

Brain imaging is one of the most important MRI appli-cations, and the application of hp-GRAPPA on brain wasstudied as well. Both high-resolution axial and sagittalbrain anatomy data were collected on a 3T GE system (GEHealthcare) using the T1 FLAIR sequence (FOV 220 mm,matrix size 512 � 512, TR 3060 ms, TE 126 ms, flip angle90°, slice thickness 5 mm, number of averages 1) with an8-channel head coil (Invivo). PE direction was anterior–posterior.

Full k-space data were acquired for all datasets, but onlypartial k-space data were used for reconstruction to simu-late PPI data.

FIG. 2. The flowchart of hp-GRAPPA.

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Design of Filter for hp-GRAPPA

Based on the discussion in the Theory section, it can beseen that the high-pass filter should be designed such thatthe energy of low-frequency components is significantlyreduced, and the filtered ACS lines still provide enoughinformation for calibration of convolution kernels. Filter 1defined by Eq. [1] gives an example. A concern about Eq.[1] is that this filter is constant along the frequency encod-ing (FE) direction and it suppresses all signals in the samePE line equally. This is not desirable because these signalscontribute to image support unequally along the FE direc-tion. It is better to suppress primarily at the center wherethe data contribute most to image support and preserve

most of the rest for calibration. A filter for this purpose isgiven by the following equation:

F2 � 1 � �1 � e��kx2�ky

2�c�/w��1 � �1 � e��kx2�ky

2�c�/w��1, [2]

where ky is the count of PE lines, kx is the count of FElines, and c and w are two parameters to adjust the filter. csets the cutoff frequency and w determines the smoothnessof the filter boundary. The definition of this filter is similarto the filter L defined in Ref. (8). This filter is called filter 2and has been used in this work. In the following text“hp-GRAPPA” refers to the method with filter 2.

In Eq. [2] the reduction of image support and preserva-tion of calibration information is balanced by the param-eters c and w. Generally, smaller c or larger w reduces theimage support less, hence the result is more similar to theresults obtained using original GRAPPA; larger c orsmaller w suppresses the image support more, but thesuppressed ACS lines provide less information for thecomputation of convolution kernels. Experimentally, itwas found that these parameters may be predefined andthe reconstruction result cannot be improved significantlyby using parameters other than the predefined values.Table 1 provides some examples of the predefined param-

FIG. 3. Results of the cardiac im-age acquired with a 32-channelcoil. Acceleration factor was 6and 24 ACS lines were used forcalibration. c � 24 and w � 12were used in the high-pass filter.a: The reference image; the re-gion in the white box shows theROI. b: The plot of relative errorsat ROI (dotted lines) and thewhole image region (solid lines).c,e: The images reconstructed byhigh pass GRAPPA and GRAPPA.d,f: The difference maps of c ande. d and f are brightened 5 timesfor visibility.

Table 1Predefined Filter Parameters

No. ChannelsNo. ACS

�8 �8

C � 24 W � 224 W � 12 C � 1232 W � 10 C � 1448 W � 8 C � 1864 W � 6 C � 24

High-Pass GRAPPA for Improved PPI 645

eters. This table was used in all of the remaining experi-ments.

To evaluate the image quality of the reconstructed im-ages, difference maps and relative errors were used. Thedifference map is the absolute value of difference in mag-nitude between the reconstructed image and reference im-age reconstructed using the full k-space data. The differ-ence map gives the distribution of error. The relative erroris defined as the ratio of the square root of the sum ofsquares (SSoS) of the difference map to the SSoS of thereference image. Relative error is one quantitative ap-proach to evaluate the accuracy of reconstruction.

For GRAPPA implementation the size of convolutionkernels was 4 � 5. hp-GRAPPA employed exactly the samesize of convolution kernels. Filter 2 was used in hp-GRAPPA with parameters c and w predefined in Table 1.All methods were implemented in the Matlab program-ming environment (MathWorks, Natick, MA). The Matlabcodes were run on an HP workstation (xw4100) with two3.2 GHz CPUs and 2 GB RAM.

RESULTS

In this section the application of the proposed method oncardiac imaging and brain imaging are presented. Theresults of hp-GRAPPA are compared with those of conven-tional GRAPPA.

Application to Cardiac Imaging

Figure 3 shows the results of cardiac images acquired withthe 32-channel coil. In all reconstructions, 24 ACS lineswere used for calibration. Based on Table 1, c and w wereset to 12 and 2, respectively. Figure 3a shows the referenceimage. The white box shows the location of a selectedregion of interest (ROI). Figure 3b presents relative errorsat the ROI (dotted lines) and the entire image region (solidlines) with different acceleration factors. The relative errorof images reconstructed by GRAPPA increases faster thanthat of the images reconstructed by hp-GRAPPA. When theacceleration factor is 6, the image reconstructed by hp-GRAPPA (Fig. 3c) has a much lower noise level than thatreconstructed by GRAPPA (Fig. 3e). From the differencemaps it is further observed that Fig. 3c also has fewerresidual aliasing artifacts than Fig. 3e. This experimentdemonstrates that hp-GRAPPA dramatically reduces thenoise/artifact level when the acceleration factor is high. Atan acceleration factor of 6 the relative error was reducedfrom 36% to 21% in the cardiac ROI. When the accelera-tion factor was low (2 or 3), both methods generated sim-ilar results.

Figure 4 shows images reconstructed by hp-GRAPPAand GRAPPA from the data acquired with a 4-channel coilat acceleration factor 3. The central 24 lines were used asACS lines. Based on Table 1, c and w were set to 24 and 12,respectively. Figure 4b–d shows the reconstructed images.The image reconstructed by GRAPPA (Fig. 4d) clearly hasa higher noise level than that reconstructed by hp-GRAPPA (Fig. 4b). The difference maps (Fig. 4c,e) furtherconfirm the reduced noise levels in the image recon-structed by hp-GRAPPA. The relative error was reducedfrom 21% to 16% in the cardiac ROI by using hp-GRAPPA.

These experiments show the advantages of hp-GRAPPAon cardiac imaging with a small (4) or large (32) number ofchannels.

Application to Brain Imaging

In this experiment hp-GRAPPA was applied to brain im-ages. Figures 5 and 6 show the results of an axial slice (Fig.5) and a sagittal slice (Fig. 6) acquired with an 8-channelcoil. The acceleration factor was 4, with 56 ACS lines; thenet reduction factor was 3. Since 56 is close to 64, based onTable 1 c and w were set to 24 and 6, respectively. Figures5a and 6a show the reference image. The right columnsshow the zoomed-in version of the region identified by thewhite boxes in Figs. 5a and 6a. The results of GRAPPA(Figs. 5e,f, 6e,f) depict excess noise. The errors in theresults of hp-GRAPPA (Figs. 5c,d, 6cd) are moderate. Therelative errors were reduced from 13% (axial) and 18%(sagittal) to 9% (axial) and 12% (sagittal). From thezoomed images it is observed that the definition of bound-

FIG. 4. Results of the cardiac image acquired with a 4-channel coil.Acceleration factor was 3 and 24 ACS lines are used for calibration.c � 12 and w � 2 were used in the high-pass filter. a: The referenceimage. b,d: The images reconstructed by hp-GRAPPA andGRAPPA. c,e: The difference maps of b and d. c and e are bright-ened 5 times for visibility.

646 Huang et al.

aries and visibility of some structures are seriously dam-aged by noise in images reconstructed by conventionalGRAPPA, but the damage is clearly reduced in the imagesreconstructed by hp-GRAPPA. These results demonstratethat hp-GRAPPA may be applied to brain imaging to re-duce noise level in images reconstructed with PPI data.

DISCUSSION

Comparison of Filters

Figure 7 shows several examples of high-pass filters. Filter1 (Fig. 7a) is defined by Eq. [1] and is the filter used inSPEED; filter 2 (Fig. 7b) is defined by Eq. [2] and used inthis work; another filter for high-pass filtering is the stepfunction, which sets the signal in low-frequency regions to0. Filter 3 (Fig. 7c) is a step function along the PE direction,which, in this example, is zero at more than half the rows(row 512 to 230) and unity at the remaining rows. At leasttwo step functions like Fig. 7c are necessary. Each functionis for one segment of k-space. Figure 7d–f shows the fil-tered axial brain image with these three filters.

When the number of ACS lines is small, only the pro-posed filter 2 is applicable. As mentioned in Materials andMethods, filter 1 suppresses all signals in the same PE line

equally. Due to this oversuppression the calibration infor-mation is insufficient if there are not enough ACS lines.Notice that the very central k-space lines are suppressed tozero using filter 3, and the number of ACS lines also mustbe large to preserve sufficient calibration information.With the shape shown in Fig. 7b of the proposed filter 2,the low-frequency information is suppressed enough toreduce image support. However, there is still sufficientinformation for calibration at the central k-space lines.Figure 7g–i shows the results of these three filters with 24ACS lines at acceleration factor 4. Because of the limita-tion on the number of ACS lines, filter 3 is not applicableand hence Fig. 7i is left empty. The result using filter 1(Fig. 7g) has significantly more noise/artifacts than the oneusing filter 2 (Fig. 7h); the relative errors are 22.5% and12.9%, respectively. These results confirm that filter 2 hasbetter performance when the number of ACS lines is lim-ited.

When the number of ACS lines is large enough for allthree kinds of filters to preserve sufficient calibration in-formation, the images reconstructed with filters 2 and3 have similar image quality. A set of step functions, likefilter 3, is used in segmented GRAPPA (9) and KIPA (10).These step functions can be arranged along both the PEand FE directions. K-space data are divided into numerous

FIG. 6. Results of the sagittal brain images. The acceleration factorwas 4 and 56 ACS lines were used for calibration. c � 24 and w �6 were used in the high-pass filter. a: The reference image; the whitebox shows the location of the zoomed in region. c,e: The imagesreconstructed by hp-GRAPPA and GRAPPA. b,d,f: The zoomed inimage of the left column.

FIG. 5. Results of the axial brain image. Acceleration factor was 4and 56 ACS lines were used for calibration. c � 24 and w � 6 wereused in the high-pass filter. a: The reference image; the white boxshows the location of zoomed in region. c,e: The images recon-structed by hp-GRAPPA and GRAPPA. b,d,f: The zoomed in imageof the left column.

High-Pass GRAPPA for Improved PPI 647

segments by these step functions. Each segment uses a stepfunction as the filter to reduce image support (Fig. 7f), andis reconstructed individually with the filtered data. Thebrain dataset was used again in reconstruction to comparethe performance of three filters with a large number of ACSlines. A truncation scheme for filter 3 is proposed in Ref.(9) (at acceleration factor 4, with 64 ACS lines, two stepfunctions are used. One of the step functions is unity at theupper partial k-space region and at upper 13 ACS lines,and is zero at the remaining regions. The other step func-tion is unity at the lower partial k-space region and at thelower 13 ACS lines). The parameters for filter 2 are pro-posed in Table 1. With these predefined parameters theimages were reconstructed using the acceleration factor of4 and 64 ACS lines. Table 2 gives the relative errors. It canbe seen that the images reconstructed with filter 2 andthose of filter 3 have similar image quality. The imagesreconstructed with filter 1 have higher relative errors than

the others. The results of filter 2 are slightly better thanthose obtained from filter 3.

The comparison of filters shows that a filter, like filter 2,that suppresses k-space signal adaptively can generate bet-ter results and needs fewer ACS lines than one filteringalong FE direction equally.

Notable Observations

It is observed that hp-GRAPPA generates a different arti-fact pattern from that generated by conventional GRAPPA.

FIG. 7. Comparison of filters. These three rows are for three different filters separately. The first column shows the filters; the second columnshows the images after filtering; the third column shows the reconstructed images with 24 ACS lines at acceleration factor 4. Figure 7i isempty because the number of ACS lines is too small for filter 3 (c). A set of step functions, like c, is used together for one reconstruction.Each step function is used for one k-space segment.

Table 2Relative Errors (%) of Brain Images Reconstructed with DifferentFilters

Axial Sagittal

Filter 1 10.7 13.7Filter 2 9.2 11.9Filter 3 9.7 12.8

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The difference of artifact pattern can be seen from thecomparison of Fig. 3d and 3f (also Fig. 4c and 4e). This canbe understood if one notices that the aliasing issue thathp-GRAPPA resolves is different from that in conventionalGRAPPA. For example, in Fig. 1 hp-GRAPPA is trying toreconstruct Fig. 1c from Fig. 1d; GRAPPA is trying toreconstruct Fig. 1a from 1b.

In this study it was found that hp-GRAPPA generatesboth less noise and fewer artifacts than conventionalGRAPPA. This is not the same as the truncated singularvalue decomposition (TSVD)-based regularization meth-ods (11–13) or regularized PPI techniques (14,15) withprior information, which use a regularization parameter tobalance SNR and artifact suppression. In all of the imagesreconstructed by hp-GRAPPA with predefined parameters,no reduction in spatial resolution was observed and SNRwas preserved.

It is also observed that if the central k-space is slightlysuppressed by the high-pass filter (with a small c or a bigw), and the image support is not actually reduced, theimage quality is still improved slightly. This observationcannot be explained from the point of view of image sup-port reduction. Further investigation should be made tofurther understand the interaction between GRAPPAweight determination and image support.

CONCLUSION

An image support reduction technique is introduced forGRAPPA. A filter is applied before and after GRAPPAoperation without modifying the GRAPPA kernel. The pa-rameters used in the filter can be predefined. This tech-nique, named hp-GRAPPA, dramatically reduces thenoise/artifact level in the reconstructed image. This ap-proach is simple and may be applied to enhance the clin-ical applicability of self-calibrated PPI. Further research isnecessary to fully understand the rationale of hp-GRAPPA.

ACKNOWLEDGMENTS

The authors thank the anonymous reviewers for invalu-able feedback, and Larry Hyler for critically reading andediting the article.

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